Angron would not have followed the Emperor if he had saved the Eaters of Cities, which is why the Emperor would not do so.
I see many people misunderstand the events of Desh'elika, arguing that the Emperor acts out of character in being so hostile to Angron, and that he could or should have helped Angron win the battle and, by extension, his favour. This is wrong, built on a fundamental misunderstanding of both characters.
If the Emperor saved the Eaters of Cites and asked Angron join him in exchange, Angron would have refused. If the Emperor insisted, Angron would fight and die if he had to; I mean hell, that was his plan at Desh'elika anyway. Once he is at the point of preferring death in an unwinnable battle to a return to servitude, it doesn’t really matter how unwinnable the battle is or who he'd be in servitude to.
The Khan joins the Emperor because he realises the choice is between death and service, a choice which he had forced upon others in the past, and accordingly he chose service. Angron was never going to choose service; All Angron wants is for him and his siblings to retire free. He wants to live on a nice little farm with them in a little anarchist commune in the middle of nowhere, and he wants to grow old happy, undisturbed and free with the people he cares about. And if he can’t have that, his background as a slave means he finds dying in pursuit of that goal to be the next most preferable outcome.
He doesn't care about the fate of the galaxy or of the human race as a whole, he doesn't care about power (outside of winning his freedom), he doesn't yearn for conquest or glory or to spread an ideal, he doesn’t believe he is honour-bound or predestined to serve the Emperor; uniquely among the Primarchs, there are no carrots the Emperor can offer Angron which would entice him. Angron’s supreme ideal is freedom, which is anathema to the Emperor.
The Emperor, on the other hand, needs Angron as much as any other Primarch; partly to stabilise the Legion genetically and partly to lead them in accordance with his plan. The Primarchs are tools, and are treated as such. If someone steals your hammer, you may try to recover it. If someone damages it, you may try to repair it. But ultimately the hammer is a tool and operates under your direction. The Emperor lets the Primarchs think of him as a father because, for some, it’s a motivator and/or method of control. But to the Emperor, they are still merely tools used to achieve the project.
He needs Angron and can’t just let him go. Not only because he is needed for various aspects of the plan, but because the project of the Imperium (divorcing mankind from the influence of the warp) cannot be opt-in; it has to be universal for it to work, and if a Primarch can just choose not to be a part of it the whole thing collapses.
So all we have left is stick, and nothing but stick; the Emperor needs to break Angron's spirit. He needs to show Angron that he is a tool created for a purpose which he will fulfil, irrespective of what he "wants", and that the Emperor can indeed force his will upon him. However, he needs to do it without offering Angron the opportunity to martyr himself, because if Angron can die free he will choose to do so. So he pulls Angron out of the final battle, denying him his martyrdom and divorcing him from the fate of his siblings. He does this to show Angron that he has no choice, that he is not free, that he will lead his legion in the Emperor's name whether he likes it or not, and most importantly that the Emperor can make him do this.
I will again refer back to the hammer metaphor; if your hammer is not working (i.e. it’s broken) then you would probably attempt to repair it before discarding it, especially if you had spent time searching for it because it could not be replaced. That the repair process may be uncomfortable for the hammer, or may not work, is a matter of no concern.
The Emperor is not kind or altruistic. His treatment of Angron is not unusual; had the Khan refused, the same fate would have befallen him. The only unique thing is that the Emperor has nothing to offer Angron. If he had something to offer he'd have been as magnanimous with Angron as with any other Primarch, and if he'd completely lacked leverage over any other Primarch he'd have been equally as callous and heavy-handed with them as he was with Angron.
Postscript
I think it worth touching upon censure, which we know happened to 2 and 11 and was considered for Curze and Angron; clearly the Emperor isn't above discarding tools which no longer work. But we also know that 2 and 11 were found and put in command of their legions sometime before their censure, so we can assume that at the very least a living primarch would be needed for a time to stabilise their Legion's geneseed. And again, from the Emperor's perspective, "repairing" Angron from a wilful former slave to a dutiful imperial general would be preferable to discarding him outright.