I wouldn't say "impossible", since there's always a way to obfuscate your Bitcoin balance from third parties and even the government itself. It's just that it'll be much harder to "anonymize" your Bitcoins when there's KYC all over the place. Governments are ramping up their surveillance efforts, to help avoid people from getting access to Bitcoin without providing their personally-identifiable information.
If you're keen on hiding your Bitcoins from plain sight, then just use a reputable mixer (preferably non-custodial) or simply convert your BTC to XMR in an instant exchange (eg: SimpleSwap, CoinPlaza, FixedFloat) for complete peace of mind. It's as simple as that. For the truly paranoid, using a VPN is a must to add an additional layer of privacy. You should always seek to change your methods, especially when governments are constantly adding new obstacles to help prevent you from "laundering" your coins. It's a good thing Bitcoin is decentralized, or it would've been compromised already. As long as you follow the necessary security precautions, you'll have nothing to worry about. Just my thoughts