I have not used Kucoin before, but there are sometimes the exchange request for KYC while you want to withdraw any amount, be it small amount or large amount.
I have been using kucoin for a long time without kyc and never experience what you have described above. I have withdraw more than 10k in kucoin last year without any requirement on their part for kyc, so if am a bit confused how you come to know this perhaps it is someone who experience it that told you because according to you... you have not use them before. But as far as I have been using kucoin, and still using them I have not experience such.