Earlier quoted context omitted.
The problem with this is that mining isn't just about reporting hash rates, it's a critical part of the Byzantine failure tolerant consensus algorithm that was bitcoin's key contribution. If miners had a lower duty cycle as you suggest, any dishonest miner could execute a majority attack with little resistance, absent some other kind of mitigation. While proofs of work are wasteful, the only alternative I know of is…
You could keep the blockchain and run with vastly reduced difficulty, but with one alteration: the next block needs to include a specific magic secret number. This magic key is unknowable in advance of a specific time, preventing workers from doing the hash work until the key is 'published'. This forces the miners to pause and not do any hashing for a set time. Now, this gets to the real issue: We need a source for t…
This would seem to lead to a situation where, after a proof-of-work block is minted, those minting POW blocks relax and those minting POS blocks march things forward for each of their accounts until they find the earliest time that satisfies any of them - at which point they simply wait until that time arrives (for themselves or anyone else playing).