Validators derive a significant proportion of their yield from proposing blocks - both proposer rewards on CL and tips on the EL. Since this leads to increased reward variability (which hurts small stakers) wouldn't it be better if there were no CL reward for proposing, or even a fee?

So at minimum the proposer fee would cancel out all the rewards received via attestations, and by proposing honestly, validators earn back some or all of that fee, plus whatever they receive in EL tips.

Similar mechanisms were discussed in the case of a negative issuance regime with stake targeting, you still need to incentivise for correct duties to be performed, so it could take the form of an upfront fee that you attempt to make back when it’s your turn to propose

Robust Incentives Group @ Ethereum Foundation

https://rig.ethereum.org

One issue of course is missed slot penalties affecting small stakers more than larger ones