The concept "not your keys, not your crypto" does not apply in my opinion when you hold the keys but the government knows about all transactions and can even tax you just for owning something. It's not your digital property if they are free to tax you for the amount they want.
The government knowing about all your transactions comes with you giving them the opportunity to know that if you plan to not get yourself involved with the government tasking trouble, you need to start up well during your accumulation process by avoiding anything that has to do with KYC before buying your crypto. Once you make the mistake of using centralized exchanges, moving your coin down to your self-custodial wallet can only help you gain full control of it to decide when to spend it, but your authorities will always crack down on you for your tax remittances.
Would you register all your crypto assets with the IRS, or trade to stablecoins and keep them away from them?
Trading to a stablecoin won't do you any good; as long as the government already has your record from the regulated exchange you purchase your coin from, the best thing to do is register with the IRS and do proper reporting to avoid being penalized by your government.
I just think it's sad that not giving up your privacy is considered a criminal offense.
That's just the sad reality, and it will be hard for the government to change from that mentality. As citizens of a country, there is nothing like privacy between you and your government; they just want to know everything about you, especially how your cash flows in and out. The crypto space that's supposed to be an anonymous place of holding and detaching your real asset from your identity is now considered to be a crime when the chain between how your coin was acquired is broken.