Well BA have taken steps on that issue by making you pay if you want to choose where you sit on the HBO fare, regardless of whether you get to check a bag for free or not...

FWIW, I don't see any real issue with the email sent to the OP. It's not like they are going to put too much pressure on someone in CE to actually check their bag, no big deal to send the email in advance if they know the flight situation and it saves them a bit of time asking at the gate for volunteers.

Question - when an airline gate checks bags, do they have to pay the same baggage handling fees at each end as for a bag checked in the normal way?

The fact that the message is not tailored to the passenger/flight isn't exactly new for BA, I've had plenty of POUG offers for LCY departures offering me lounge access, extra legroom and a wider seat...