Let's say the winner of the block reward is decided by a lottery of some kind that forms part of the protocol. And in order to claim the reward he needs to do all the other - existing - things, which are currently external to the hashing process, yet considered part of the mining process.
Would that be a bad idea? If so, why?
Proof of stake attempts to do that.
It's a good idea because it avoids all the energy consumption required by brute force mining. It's a bad idea because all implementations up to date suck and are not as secure as Bitcoin's proof of work mining.
There's a lot of literature on that, search for proof of stake and "nothing at stake".
But it doesn't belong to "technical support" section, look in the altcoins section