I think the best solution would be to properly tax carbon. That way Bitcoin miners would either become unprofitable or move to greener energy.

I think cap and trade can be a good idea, the problem is getting all the countries in the world to sign onto it. Any country that doesn't ends up with a competitive advantage. But if you somehow got them to all agree, blockchain actually provides a perfect way to build a cap-and-trade system that every country can participate in, transparently, without having to trust one country or group of countries to run it honestly. That's the essential problem blockchain solves: administering systems trustlessly.

Bitcoin miners do by and large use green energy since it tends to be the cheapest (off-peak hours from over-provisioned grids). If electricity gets more expensive, it doesn't mean it becomes unprofitable to mine, that's only one side of the equation. The other side is how much people are willing to pay to get transactions added to the blockchain, which is a number, on average, that has increased year after year. Not that you ever need to make an on-chain transaction, with Bitcoin lightning you can do transactions off-chain while getting much of the security of on-chain transactions. You can move money internationally in under a second for pennies in fees. And it works just as easily as venmo. In fact, if you have cash app on your phone, you already have the ability to use the lightning network, though it's a custodial wallet (meaning you are trusting cash app not to take/lose your BTC).