IMO this is not a big problem. The problem is not if a 0 value ever enters the mempool, it's if it is never spent. And even if C2/P1 goes in, C1 still can be spent. In fact, it increases it's feerate with P1's confirmation so it's somewhat likely it would go in. C2 further has to be pretty expensive compared to C1 in order to be mined when C2 would not be, so the user trying to do this has to pay for it.

If we're worried it might never be spent again since no incentive, it's rational for miners *and users who care about bloat* to save to disk the transaction spending it to resurrect it. The way this can be broken is if the txn has two inputs and that input gets spent separately.

That said, I think if we can say that taking advantage of keeping the 0 value output will cost you more than if you just made it above dust threshold, it shouldn't be economically rational to not just do a dust threshold value output instead.

So I'm not sure the extent to which we should bend backwards to make 0 value outputs impossible v.s. making them inconvenient enough to not be popular.

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Consensus changes below:

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Another possibility is to have a utxo with drop semantics; if UTXO X with some flag on it is not spent in the block it is created, it expires and can never be spent. This is essentially an inverse timelock, but severely limited to one block and mempool evictions can be handled as if a conflict were mined.

These types of 0 value outputs could be present just for attaching fee in the mempool but be treated like an op_return otherwise. We could add two cases for this: one bare segwit version (just the number, no data) and one that's equivalent to taproot. This covers OP_TRUE anchors very efficiently and ones that require a signature as well.

This is relatively similar to how Transaction Sponsors works, but without full tx graph de-linkage... obviously I think if we'll entertain a consensus change, sponsors makes more sense, but expiring utxos doesn't change as many properties of the tx-graph validation so might be simpler.