This is why having a wallet that generate new addresses after each transaction is some how best for tackling this hilarious KYC demands from exchanges. One can easily make claims to anything of their choice as their source of income so has to protect keep some part of their dealings even more anonymous or what do you think
How about exchanges in some countries that will require all their users to register the noncustododial addresses they are sending crypto to. But change address can help privacy while making use of noncustododial wallet. Also, if you change address but still send from an exchange, the exchange can still possibly link addresses.
Every single site does require the same information now a days you can always look for other places like samourai wallet if you are not sure about going in for a place needing the kyc and there are still other options that you can use for sure like : paper wallets etc. If you wanna stay afar from the sights of the government then that's the way to go.
Not only Samorai wallet, noncustododial wallet if to have full control, but best to go for the ones with change address. If I should recommend a wallet for someone, I will prefer to recommend Electrum wallet, but Samorai wallet have some privacy feature like ricochet. Noncustododial wallet can be used to have full control but most of them only can be used for privacy, before they can also be used for privacy, it needs some technical knowledge.