Cutting your guest list is either the best lever you have or the worst one, and it depends entirely on the venue
I've been pricing venues for my own wedding all year and I had this one backwards for months, so I want to lay out both halves of it.
The usual case first. At most venues a big chunk of what you're paying is fixed. Staffing, setup, delivery, the minimum order, the room itself. Those barely move whether you're at 150 or 90. So when you cut people, your total drops a bit and your per person cost actually goes up, and you gave up thirty guests for maybe fifteen percent off one line. That's a bad trade, and it's why the standard advice is to change the day instead.
The exception is venues where you're buying almost everything per head, and some of the big prestige spaces work exactly this way. There's a large fixed base you cannot negotiate: the room fee, mandatory security, valet, sometimes a furniture removal fee. And then everything else scales with your count, including the rentals, because every chair, linen and place setting is a per person charge. There's no fixed staffing to spread out, because you're renting the staff too.
At a venue like that, guest count is the only lever you have. You can't change the caterer because they hand you a list. You can't source rentals cheaper because they're per head anyway. You can't negotiate the security requirement. So the number of people is the entire game, and going from 170 down to 130 can be twenty thousand dollars.
The way to tell which situation you're in is easy and nobody does it. Ask for a quote at your target number and a second quote at thirty fewer, then look at what actually changed. If the total barely moved, your money is sitting in fixed costs and you should be changing the day or the time instead. If it moved a lot, guest count is your lever and everything else is noise.
I wish I'd known to ask for two quotes instead of one. It's the same email and it tells you which of two completely different problems you're actually solving.