Usually has exchange not requirement with KYC such as MEXC and Kucoin but last update both exchange can't trade if not verifying KYC and currently almost all CEX exchange have requirement with KYC.
Because with more regulations on this market and stricter regulations on AML, costly fine fee on exchanges like Binance, Kucoin, centralized exchanges will go first to save their platforms and avoid being sued with expensive fees. KYC will soon become a new standard on all centralized exchanges first in the USA, then Europe and globally.
I don't know any CEX exchange without requirement KYC and have lo fees fees trading or withdrawing fund, some exchange without required KYC seems less volume transaction on their market and make difficult for trading there, better update your document ID and verifying if want trade on top exchange market with huge volume transaction in daily day such as Binance, Kucoin or Huobi exchange.
If you have small fund, you can use them but you have to consider about security and safety of your account and fund. With smaller exchanges, you can avoid KYC but if you see safety of your fund is main concern, you might not use them but will choose top exchanges.
Huobi, I don't recommend this exchange because it has shady activities recent years. You will not know what will happen with an exchange like Huobi.