Awesome idea and ensuing discussion!
One of the bigger advantages of this approach imo is that it massively increases cost for builders and proposers to vertically integrate, but thats more to do with the concept of proposer auctions than the burning aspect.
Although this issue exists currently w/o burning, builders could multilaterally agree to never bid higher than some threshold or % of MEV and bypass much of the burn. I think it’s unsafe to assume there will always be an altruistic builder offering the max MEV it has private access to.