I am a bit worried about the possible consequences of changing PoS into “Proof of MEV extraction” (which I’ll just call PoM from here on). By this I mean that the actual builder of a block would be chosen in that way, regardless of the fact that the proposer is chosen in the normal PoS lottery.
The main issue I see is that PoS (as PoW) distributes outcomes uniformly over the global pool of resources, but PoM does not. If someone has 1% of the stake, in PoS they’ll get to build 1% of the blocks, but in PoM there is no clear way to have (probabilistically) guaranteed access to a small percentage of the blocks by committing an equivalently small percentage of the globally committed resources, because it’s not a brute force search but one where algorithmic sophistication makes a huge difference. The problem with a game dominated by the latter is that “a little bit of algorithmic sophistication” does not get a little bit of the blocks, it doesn’t get almost any of them, and that access to “sufficient algorithmic sophistication” is a much higher barrier of entry than some capital and a little bit of technical knowledge (as in PoW or PoS).
How many entities even are there that could truly compete in such a game? Assuming there’s not many, PoM could end up hugely centralising block production, which is obviously very problematic