But I'd expect it to be cheaper then - as it stands, it's identical to the (already) outrageously expensive prices at the ticket booth, and onboard (apparently a £5 surcharge exists which I've never been charged). I loathe the Heathrow Express - if there's more than one of you, it's almost better to just book a mini-cab local to where you live.
BA's app on the other hand is rather good. When you say Executive Club membership is required, it's free to join and hardly exclusive as the name suggests. The arse of it is in the airports that don't accept it, as you point out, but not surprising as they're well outside BA's control - I'm impressed they've managed to influence so many airports already.