I see.
So the problem is that the block proposer is not sharing money with the pool.
One unfortunate weakness is that if I am MEV extractor, then using a scheme like described above will force me to leak information about MEV value extracted. If I found a new way to extract MEV I may not want other people to even know extraction is possible. So I may just bid a little higher than others and pay the rest to the proposer privately.
A much better scheme as I mentioned before is to use threshold encryption by a committee. There is simply no MEV under threshold encryption. A Uniswap running under threshold encryption scheme will be way more attractive for users since there will be no hidden fees due to MEV.