We’re not trying to discourage proposers from receiving private bids! In the analysis of MEV burn I would assume that all proposers are willing to receive private bids 
If all bidders capable of extracting a specific piece of MEV collude then it’s game over, with or without collusion with the proposer, as well as with or without MEV burn. As argued in the “colluding builders” section under “late bidding”, a cabal of colluding builders can keep all the MEV for themselves (e.g. equally split the MEV among themselves instead of racing towards zero margins). The good news is that 100% collusion within a permissionless set of competing builders is hard—the equilibrium is a race to zero where individual builders defect.
The design is secure under an honest majority of attesters, similar to EIP-1559. (See the section titled “honest majority” under “technical similarities with EIP-1559”.)
I disagree with this premise—IMO it’s likely net positive for validators to embrace the redistribution of MEV. See the section titled “side note for validators” under “staking APR”. The crux of the argument is that ETH-denominated returns are tied to the cost of money, and USD-denominated returns (as well as the USD-denominated principal) should actually grow.