You can begin to obscure the source/chain of transactions as you use things like Lightning or coinjoin (although I believe chainalysis watches Lightning now too).

The main issue with KYC is not the link between specific coins and your identity (unless those coins implicate you in some way).

It’s more that your “purchased Bitcoin” amount is on record and can be leaked/hacked. It also creates the assumption that you still own those coins (ie control the addresses where they end up).

If the IRS asks you to prove ownership or else pay capital gains tax, you don’t want to run afoul of those laws.

And if KYC’d coins are otherwise used illicitly, it’s easy for law enforcement to solve those cases