I think this is possible, the hard bit is identifying offenders, but it has a solution:

When cheating occurs, the block headers for both the beacon chain and the execution chain are posted to the contract. These are self verifying data structures in that you can see which validator signed the beacon chain header and what block hash it was for, and you can then look at the block hash and payout address in the execution block header. The contract can verify all of this (I believe you can verify BLS signatures inside of the evm).

So once it can verify it can slash the offender if someone posts the evidence.

Participants would need to post a collateral that can be slashed and they would need to be extra careful about not making mistakes with the fee recipient (which already appears ambiguous, suggested fee recipients, MEV etc). I think this would turn most people off.