If you are going to use a big exchange in the future then you will need KYC. The only other way to get BTC will be on the black market. Would that put you off?
Many people do not realize that they have entered a dangerous realm and easily steal their data assets because they arbitrarily verify their personal data. Nowadays, it is not possible to use large centralized exchanges. and reputable. So privacy is exposed when you are using one of them which requires KYC. If you trade P2P then there will be liquidity and fee issues. Worry more, you won't find your desired trading pair. Only holders can prevent their privacy who is not associated with any centralized exchange. Personally I would use centralized exchanges to hide my coins. it's the best way not to be bothered by the crypto laws in my country.