Eloise's Financial Situation
There seems to be a somewhat common belief that Eloise, being a woman in the Regency era, needed to marry for financial security, and that Violet's push for Eloise to get married is the case of a pragmatic Violet trying to secure a deluded Eloise's future and ensure she is provided for. The basis for this belief seems to be that single women (or at least, single women from families too high class for women to work) did not have money or property of their own, and that the money put aside for their dowries was intended entirely for their husband's use, not their own, and therefore, if they never got married, no money would go them, even if money had been intended to be for their use.
The dowry's primary purpose, above all things, was to ensure that a woman was provided for. In husband hunting, the larger the dowry, the greater the net you could cast over potential husbands. Once married, there would be marriage settlements, which would determine how much of woman's dowry or "marriage portion" could be accessed by the husband. The marriage contracts were the only way a woman's property would remain her own, and they caused a great deal of debate and haggling between families and lawyers. As a rule of thumb, a lump sum would be put on the woman. It would be invested, and her pin money would likely come from the proceeds (husbands might also contribute to their wives' marriage portion). Pin money was money a woman could access without her husband's say so. Whereas the husband could not access the lump sup of money (which might also be kept protected by trustees, such as male family members of the wife) he could claim interest from it, or money the wife earned or inherited after marriage. If the woman is widowed, that lump sum then ensures she is provided for, as she would live off the interest of that, and any other money her husband leaves her. For a woman whose income depended on her husband's profession, such as clergyman or lawyer etc..., a dowry large enough to live on was essential for her survival.
The point of the dowry wasn't ultimately "marry this woman and get a large chunk of cash as a reward" (although if families were looking for advantageous marriages that was a bonus), it was to ensure a livelihood for the woman, and if she married, making sure that whatever her husband did, whatever he earned, saved, or spent, she would at the end of the day have some financial security.
The dowry was money given to a woman at the point of marriage, but that isn't to say if she never got married, she wouldn't receive any money, or that spinsters had no property rights. I explained roughly how dowries worked in regards to marriage to demonstrate how the intent behind them was to provide for the woman. The point of that money was to ensure a woman was provided for. With such an intent, if a woman had a family who had means to provide for her, they would, whether that be through supplying a large dowry to attract husbands, or leaving her legacies in a will. The money that would go into the dowry did not magically disappear if a woman never married, and the family's desire to see her provided for and safe did not fade away if she became a spinster, unless the family in question was spiteful and dishonourable, or made some stipulation that she must be married in order to receive her inheritance (which was not standard practice, and more the set up for a romance novel than anything else.) If a family had enough money to provide a woman a lump sum to live off, they could, regardless of her marital status. There was no laws preventing them, and the social expectation was that brothers and fathers would ensure the woman's livelihood, as much as they could afford, which in the Bridgertons' case was a lot.
Provided Eloise's father or Anthony did their socially expected duty to Eloise, Eloise would in many ways be better off financially than her married sisters. Spinsters and widows actually had better property rights than married woman. Apart from whatever lump sum put aside in the marriage contracts, a married woman had no property rights. Everything she earned or inherited became her husband's property. This is because married women were "covered" by their husband's legal identity, and did not exist as their own separate entity. Meanwhile, an unmarried woman could own as much property and have as much wealth as any man.
Wealthy spinsters, living of their own fortunes, could and did exist. There was no law in place, no practise or crushing societal convention, that would place restrictions on what Eloise could inherit, or have settled on her as a single woman. Her family has the money. Her family has the intent to see her provided for. Her family have the means to provide for her, married or unmarried. Therefore, excepting some bizarre plot device to put pressure on Eloise to marry, unfounded by an historical fact, Eloise's financial status is secure.
We know there is money for Eloise's dowry. Therefore there is enough money for Eloise's general livelihood. As Anthony described Daphne's dowry as "ample" (therefore indicating that Eloise's was large as well), her dowry must be enough for her to live on, and live a genteel lifestyle. It would not qualify as "ample" if not.
As the desired "goal" for women was to marry, their fortunes, the money put aside for them, might generally be spoken of in terms of getting them a husband and supporting them after marriage, because the general plans is for them to marry and have the money put aside for them put to use as dowries. But that does not mean the money disappeared if she never married or the desire of Eloise's family to see her provided for, which was the motive for giving her a dowry in the first place, would disappear too.
Now, is Eloise's dowry "her's" at this point in the story? That really depends on whether or not the money intended for her dowry was labelled as such by Edmund in his will. If so, then that money is hers. That's her inheritance, and it became hers when Edmund died. Currently, Eloise is underage, and her money will be protected and controlled by trustees, most likely her male next of kin, in this case Anthony, and perhaps her other brothers as well, (Georgiana Darcy was left under the care of her brother Mr Darcy, and Colonel Fitzwilliam). Once Eloise came of age, the money would be under her control. Now, a father or anyone leaving money to a woman might try to protect the money they leave a woman from fortune hunters by putting additional protections on it, (so if a woman was kidnapped and forced into marriage, or seduced by a fortune hunter and eloped without getting lawyers involved, her money would still have some protection) but this was not a necessity, and a woman could in theory control her finances as much as a man. She could partake in business deals, buy, spend, invest, as much as she liked.
As Edmund was depicted as a loving father and responsible family patriarch, it's highly improbable that he did not oversee the provision of all his children. Therefore, the most likely scenario, the one most in keeping with his reputation as a good man and father, is that since Eloise was born, money was being put aside for her, likely into trusts which would increase through investments, to ensure her future, and yes, be used as a dowry to attract husbands, which was the preferred outcome, but fundamentally, to ensure she had something to live on.
If for some reason Edmund never did put any money aside for Eloise, or specify in his will about what was to be provided for her, then that duty would have fallen onto Anthony. And this would, one hundred percent, no ambiguity, have been his duty. As head of the family, seeing to the security and welfare of his sisters was one of his most important responsibilities, and as we see throughout the series, one he takes extremely seriously. And the way to ensure Eloise was provided for was to have money legally earmarked for her provision. It would either have been dishonourable or a major oversight, and either way extremely out of character, for Anthony not to do so.
So to sum up, does Eloise need to marry for financial reasons? Is Violet's crusade for Eloise to marry a pragmatic endeavour driven by her desire to ensure Eloise is financially provided for? No. Eloise comes from a wealthy family. Eloise's family has a large enough fortune to ensure a lump of it could be put aside to ensure Eloise is provided for throughout her life. The laws of the time allowed money to be settled on women, and for women to inherit land and property. The expectation of the time would have been for the Bridgertons to provide for all the girls' futures, including the unmarried ones. It would only be a financial necessity for Eloise to marry if Edmund failed to make provisions for Eloise in his will, or Anthony failed to do so, which would have been failures on their behalf as heads of the family.
Eloise's family had the money to provide for her, married or unmarried. The laws at the time allowed them to provide for her, married or unmarried. The expectation of the time was for her family to provide for her, married or unmarried.
RE: The Show's accuracy. All the above is based on historical fact. Bridgerton has been drifting away from anything historical the longer the series went on, and it's reached the point where the writers are just saying whatever, and sometimes present circumstances as being the exact opposite of what was the case. For example, Benedict said that whereas it was improper for men and women to dance more than once together, but he points out a married couple who are getting away with it because they're married. This wasn't the case. It was a faux pas for husbands and wives to priorities each other's company too much when in a setting like a ball or a dinner party. This is because this was the time they were meant to spend entertaining and being gracious to their neighbours and society, they already had time to spend on each other at home. Another case, and this one so wrong it was laughable, was the seating chart lesson. According to Hyacinth, married couples were sat near each other, spinsters and old people were shoved off to the side, and debutantes and suitors were sat together to encourage courtship. No. This was just...no. Again, husbands and wives were always sat separately, because they were meant to be socialising. The host and hostess would be seated at the opposite ends of the table, and the most important guests would be sat beside the hosts. The less important the guest, the further they sat from the hosts. This was determined by social hierarchies (rank, title, lineage, social standing, profession) although if the dinner was held in honour of one particular person, perhaps a new bride being welcomed into the neighbourhood, they might receive preferential treatment. So yeah, Bridgerton has a habit of twisting things around and saying whatever, and I would only be half surprised if next season they announce that single women couldn't own property, but married women could, just to give Eloise a motive to get married, but this would be total bollocks.