Unfortunately we have collectively decided that solving hashes is a better use for clean energy

Maybe we could start minting coins or NFTs from captured CO2?

There is already similar stuff being done as part of tracking for carbon credits. i.e https://www.forbes.com/sites/forbestechcouncil/2021/08/16/th...

This would be an interesting approach! Not sure how it would work in practice, but it's a fun thought...

And there could be inherent value there, especially as a carbon capture tax credit. Instead of proof of work or proof of state, it's proof of capture. You'd have to put together some kind of distributed capture hardware, but... That's maybe possible with current tech?

Unfortunately the fact that it has a clearly measurable value means it's price is pegged to that value.

If this token gets you $100 worth of carbon emissions, it's hard to justify a price higher than $100. If the token gets you absolutely nothing, then the value is absolutely arbitrary - enabling spectacular rise

What if you tied it to a desktop carbon capture device (understood that these don't really exist currently)? Doesn't even have to be particularly efficient, nor tied to carbon credits.

The reason we don't have clean energy ready to use is that the cost of renewable generation plus storage is currently higher than the cost of burning natural gas. If you add the cost of capture to the cost of natural gas, that's plausibly not going to be the case anymore. And then it's more cost effective to build storage than capture.

That's the point though? You use carbon-capture as energy storage (when you have excess clean energy), and you can release CO2 when you don't have enough clean energy. In an idealized process, you basically produce coal as a form of "energy storage".