Given the proposed fixed signature size, It seems better to me that we create a SIGHASH_WITNESS_WEIGHT flag as opposed to SIGHASH_WITNESS_DEPTH.
Mark, you seem to be arguing that in general we still want weight malleability even with witness depth fixed, but I don't understand in what scenario we would want that.
It strikes me that is most scenarios all parties signing an input would do so after an execution path through the script has been agreed upon by all parties, in which case the witness weight can be fixed.
In rare cases where the smart contract requires that some parties sign in advance of the decision about the execution path (for example, I'm thinking about delegation here, but I want to keep my remarks general), we wouldn't want to fix the witness depth either.
A SIGHASH_WITNESS_WEIGHT would prevent all possible malleability that would modify the transaction's fee/weight priority (at least for that one input), and greatly reduce the overall attack surface of witness malleability issues.