It seems to me that with this mechanism, the supply of 0x03 validators will expand and contract with the value of the MEV. If MEV increases tenfold, the supply of 0x03 validators will expand rather close to tenfold, etc. It seems more intuitive to avoid capital inefficiencies by also letting 0x03 validators participate in consensus, and to keep the supply/proportion of 0x03 validators fixed, varying the fee for being eligible for builder selection. The simplest changes are thus to keep 0x03 validators staked, and to keep a fixed proportion of 0x03 validators by running a 1559-style auction to set the fee taken out each epoch for being a 0x03 validator. The fee is burned. It’s like ABPS, but adapted to concern only 0x03 validators, targeting a lower proportion.
Note that 0x03 validators will still need to sell the right to build the blocks rather often, because the builder able to extract the most MEV from the block won’t always be selected (albeit this will then be done out-of-protocol).
In any case, the concerns both you and Julian raise seem rather important. In my view, slot-auctions could be great for tackling the free option problem. Although there are then other issues to go through, they could potentially be resolved.