Some of the trusted and known exchanges before now requires a KYC such as Binance and currently now with not having a restriction with their KYC is the Kucoin which is one of the exchange support different coins too. For their restriction of transactions.
KuCoin users that complete KYC verification will enjoy higher daily withdrawal limits. The new withdrawal limits are listed below.
Verified Individual Account: 100 BTC per 24hr
Verified Institutional Account: 500 BTC per 24hr
Non-verified Account: 2 BTC per 24hr
If you are not a large investor this is suitable for you but if not i guess you need to pass with their security of KYC.
https://www.kucoin.com/news/en-complete-kyc-verification-to-enjoy-higher-withdrawal-limits
Kucoin is the best exchange but there are also other exchanges which also give a limited service for those who have not KYC verified accounts. But if you want to use without limits then DEX are the best option.