They do of course know when they should mint and will always "win" assuming that they do (only one random minter can realistically be the "best one" for each new block although in my implementation there is a small chance of "collision").

The question of incentive becomes more of an issue should the best minter not mint and then no-one else wants to (although I think in reality this wouldn't occur unless the platform had been basically abandoned).

Perhaps you are thinking this approach has a Sybil problem but as account creation is strictly controlled (by a much harder proof of work that has to repeatedly occur at a regular interval) then it becomes increasingly more difficult to create Sybils (so POW is being used to prevent Sybils but accounts are being used so that intensive POW is only needed infrequently).