I don’t think they would necessarily be cheaper, they would still be competing with all other transactions.

Something Shinobi said on WBD (with a listen if you haven’t already) was that not having visibility about what’s going into a block can be an issue if you need to make a transaction ‘now’ If you don’t have a clear picture of the mempool you don’t know what you need to pay to get your transaction confirmed.

The start of the whole thing was to do with a layer 2 that needed 140 bytes in OP_RETURN rather than 80.