One reason for giving the full boarding pass is that LGW and LHR T3 don't have Ready to Fly and therefore it's OK to do the passport scan at the gate or at the lounge. In the reverse direction, USA to Europe, the DHS requirement for a passport scan also exists, and with the make up of USA airports it's difficult to avoid people doing some of the scans on departure right at the gate. Moreover in the direction to USA, people may be connecting from other airports and need to show their onward boarding pass to get through a control point.

There is a mechanism to do your own scan but it's for iOS only, not Android, they recently changed the message to make that clear. I'm not sure it works that well, but for ESTA passengers it should be the way forward - BA doesn't market this option very clearly, as per usual. But another reason for issuing a full boarding pass, even though it won't get you airside without the scan, is that you can use it at the Kiosk and scan the passport in yourself. This works both at Flight Connections and in the main landside check-in area, but not (unfortunately) Flight Connections UK.