bitcoin has 0 carbon footprint because it is a network and bitcoin nodes, wallets, and bitcoin miners don't produce anything at all.
the electric companies on the other hand that are producing electricity have a terrible carbon footprint. so maybe you are asking the question in a wrong place!
Electric companies produces electricity to satisfy the demand created by Bitcoin miners. The existence of Bitcoin incurs carbon footprint; nodes, wallets and miners all uses electricity. It's like blaming the airline companies for their horrendous carbon footprint but not the travelers who creates the demand for air travel.
I really don't think this is an issue with Bitcoin in the first place nor would limiting the miners help. It would just make Bitcoin less secure.