Expanding on proposer/notary separation

So notaries have an incentive to be proposers. So while there is a better incentive alignment as you outline, what’s preventing a similar scenario to Exploring the proposer/collator split happening to notary-proposer-executors becoming the dominant or only player compared to proposer-executors? Additionally if notaries are randomly shuffled per shard it seems that it would still be advantageous for notary-proposer-executors to act in all shards, favouring supercomputers.

Also it would be good to see more detail on the randomness function for proposer selection, however I understand that is another topic in itself.