I've used Kucoin and Binance. In my experience, They are both 1 time KYC only with not so strict policies. I've never experienced any hassle on both centralized exchange in terms of KYC. I've heard some cases that binance is asking for re-KYC on their P2P trade if there's a problem that occur on the transaction, For example you transacted with a potential scammer, There's a chance that binance will ask for a re-KYC for investigation and to settle things.

Though both exchange is good, Remember that I've been using both for a long time and I still haven't ask for another KYC. Just be careful.