I think that you are overlooking the densification of SH that has taken place. In LCCs it is less of a problem because of the chargeable large cabin bag policies. BA removed proper galleys and toilets and shoved in extra seats and this is the result.

Airbus do have a very good solution for large cabin bins on A320s that store roll on luggage on their sides.

BA either needs to restore proper galleys/toilets on SH or pay for the Airbus cabin locker retrofit to solve a problem primarily of its own making. This and the A350LOPA are down to the Alex Cruz era.

BA has transfer Pax, LCCs don't so the solution is not to impose LCC baggage policies.