I'll chime in before @TBTB comes in and tells everyone that they are stupid and only he knows the answer to everything (at that point I'll quit watching this topic as I've done with every other topic he has ruined - and he ruins every topic he posts in basically).

The relationship between "reward" and "minting" could be made less "one-to-one" but more statistically probable if you mint more blocks (thus providing an incentive to mint but not even needing to be POW).

You need ways to discern "winners" if you aren't using POW as the only measurement (although I think some amount of POW is going to always be required to help prevent the NAS attack issue which I've discovered can even occur "by accident" when using different approaches).

This is a key part of the CIYAM blockchain design (which I am not going to discuss here, however, unlike some others it isn't some silly conjecture or "academic breast beating" but already published open source code which it seems @TBTB is actually unable to understand which rather pleases me).

As a simplistic idea imagine that a block reward only occurs every X blocks but is more likely to favour the minter that has produced as many of those X blocks as possible (and also imagine that rules prevent them from being able to produce all of the blocks).