This checking of boarding cards is something cabin crew at BA have been told to do, as Shadow Purser says.
One crew member was suspended because a CAA inspector boarded and they hadn't checked their boarding card so for some posts to suggest that they could give a long list of airlines that don't do it is interesting. Also surely even airlines that don't have seat allocation give you a boarding card prior to boarding which has the flight number and date on it?
If not why is BA being told to do it if no one else is doing it?
Or is it just a rule that is open to interpretation.