Could the government legally restrict me from solving a math problem?
If mitigating the CO2 produced by using some energy isn't priced into that energy, that's the fix. We absolutely need to incorporate externalities into prices.
No, in the same way there isn’t for money laundering or wire fraud.
Calculating a hash for Bitcoin and then broadcasting it assumedly has the same level of First Amendment protection as calculating a hash for someone else's password and then broadcasting it.
They can 'regulate' it by banning Proof-of-Work mining for 'climate change' reasons and then it will be outlawed or heavily taxed, just like in China, Kosovo, Kazakhstan and possibly Russia.
Sure, Bitcoin (and any other cryptocurrencies) can't be totally 'banned', but enough to discourage mining and using PoW cryptocurrencies via legislation or taxes.
None of this will happen, as governments aren't this united. Even within the US there's crypto-friendly and crypto-hostile states. Right now, Bitcoin is explicitly recognized as an asset/commodity, not as a currency. Property, not a security.
There's definitely regulation pending regarding crypto. In particular, many non-Bitcoin cryptos are likely securities. Stablecoins backings are to be regulated. And there may be mining regulation where it's not outright banned, but (CO2) taxed.