I got the idea, but there many problems such as :
1. How to choose/select which miners will generate a new block based on their "proven" computation power in decentralized way?
2. How to make sure the miners have actual ASIC all of the time, not only rent ASIC when on competition?
3. What happen if the chosen/selected miners don't do their job?

I'd rather choose another consensus algorithm such as PoS, DPOS, BFT or PBFT if avoiding high electricity usage is the main goal.
Also, i think your idea only benefits miners since they can mine altcoin while the "competition" don't happen and they still "waste" lots of electricity while mining the altcoin.