Sudden mandatory KYC(disabling withdrawals if you don't submit KYC) has happened in the past already and I don't think it's impossible for the same to happen to non-KYC exchanges like Binance.
You are right, of course, and I should have been more clear with my statement. I wasn't advocating for using centralized exchanges without completing KYC - quite the opposite. Indeed, if you are going to resign to using a centralized exchange for large volumes of money, I would be completing all their demanded KYC and background checks first to try to minimize the risk of running in to the situation you describe. I was rather advocating for not using centralized exchanges at all, and sticking to platforms such as BISQ or localcryptos which do not require KYC in any shape or form.
I'm finding an other way to deal with my transaction even if it is costly. I'd rather to take a costly fee than to exposed my identity in danger.
It doesn't have to be costly. There are the platforms I have described above which have very minimal fees. You can even trade peer-to-peer on the forum, and once you have built up a reputation and are trading directly with other trusted users without the use of an escrow, the only fee you pay is a couple of cents in the transaction fee.