One caveat is that without a flexible signature hash you cannot batch the incoming HTLC-success transactions. It may be the case that you have one fee-infused HTLC-Success transaction, and that is enough to pay for the whole package of commitment transaction and other HTLC-Success transactions.
I suspect from average mobile wallets this isn’t much of a concern or desire, but just noting.
And if the mobile wallet has a utxo to use, they can still do the batching.