Unless there is some funny things going on around you account and the coins you deposited in them, they will not ask for KYC and there is never a complaint from any legit users regarding any issues with the site even when they are withdrawing their money and the only issue i remember they had was when there was a DNS hijack and they locked the accounts even with two factor authentication and while contacting the support they took swift action and was able to recover the account.
If there is no signal of abusements on the platform, multi accounts, for example; or there is no huge withdrawal, KYCs won't be required by Stake.com. There is only one thing should be considered if someone think that they might do huge withdrawals in the future, in such withdrawals, KYCs will be asked, but if they don't want to do KYCs, they should have detailed plans to withdraw their funds gradually, not immidiately at a single withdrawal.