Two versions that I experimented with. One is where the incoming POW hashes contribute to hashing power for some blockchain mining. An alternative "pay as you use the API" system.
The other using hashcash. Just a way to slow down abuse.
Both, however, suffer from the downside that many/all "ASIC resisting crypto mining" suffer from as well: the cheapest CPU power is CPU power from machines/power you don't own. Botnets, viruses, trojans etc.
So such a mechanism to throtthe or protect APIs won't hold back spammers and abusers for long.
You might correctly claim clean energy is often cheaper, but you must also consider the regions in which they'll get away with nefarious activity, and whether those areas have made the investments into making clean energy cheap.
Hmm, I don't get this, surely all actors will want the cheapest energy, no? The problem being the underlying one, that the dirty energy doesn't pay its externalities and is thus cheaper than renewables.