Just one datapoint from a different airline (one that I fly even less frequently than BA) from last December.

FRA-AMM flight has been delayed. Pilot announces prior to takeoff that he personally had two choices: wait to finish loading bags, by which time the crew will have timed out and we'll all have an unplanned night in FRA, or take off without the bags. He promised more information later in the flight. He emphasized repeatedly that the decision had been his.

During the flight, more announcements, including suggesting that people start go online as soon as we landed. I actually didn't pay much attention because I only had carry-on, but there's a way to speed things up online - presumably the address(es) where you will be so that your bags can be delivered instead of waiting in a line late at night. He even announced where in the baggage claim area people should go and said he'd make sure a rep was there to help.

On landing, more profuse apologies and more reminders that the pilot took sole responsibility for deciding to go without some bags instead of cancelling the flight. (Given that this was heading into Christmas, I don't even want to think what our chances of a timely rebooking would have been like).

IRROPS happen - it's how the airline handles them that makes all the difference.