You might be responsible for paying unrealized cap gains tax in the future if that ever becomes a thing. You could be legally required to give your Bitcoin to "approved custodians". If you "lost" it you could still potentially be on the hook for that or at least bring extra unwanted attention and scrutiny.

I'm thinking worst cases, but who knows? Maybe it won't ever get quite as bad as that, but I value the peace of mind of knowing that it isn't even on the table when you acquire without KYC.

Not even mentioning the possibility of $5 wrench attacks when the general public can potentially see how much Bitcoin you've purchased