A lot of movement will not only affect sound (listen to anything with sustained notes), and is really hard on your cartridge and the record itself (but if it’s warped that damage is fairly moot). I mean if you don’t care, that’s fine, but why spend any money beyond a $20 Crosley if you don’t. Anyway, slow, rolling minor warps are less concerning than the acute, jump-style (like pry warps).
Think of it this way. Each stylus needle has a recommended manufacturer lifespan. When that needle moves up and down or side to side more strenuously than normal, that lifespan decreases faster than normal.
FWIW I don't mind slight warps that don't affect playback, but I do care about drastic warps even if I don't hear it. Obviously everyone's tolerance of slight vs drastic is different.
I just don't want to have to oven every single record I have (which beyond taking hours or even days could cause a lot of damage to the record and sound) and I still wanna listen to the records I have
Durability of your suspension is going to vary by cartridge. It’s built to handle a little (obviously if you’re running some sort of $Texas priced cart you’d want that to be limited to nothing). But the weight on your tonearm is pressing that cart down at a preset force. When you hit the top of a warp that weight is still there, and the suspension collapses at the same time the arm rises.