I can sort of understand their argument that interlining on separate tickets creates liability problems without any concomitant increase in revenue, but the better solution would be to just not screw up on baggage handling as often as BA seem to in these situations.
I haven't read all of the middle of this thread so the point may already have been discussed, but BA potentially faces significant customer inconvenience and operational hassles in implementing such a rule given that LHR is its hub and the UK isn't in a larger immigration bloc. As a result, a pax who needs a UK visa transiting from one non-UK point to another on separate tickets ends up in the soup if they can't get through UK border control to collect and re-check a bag. Likely a rare case, but perhaps not that rare for pax connecting revenue and award bookings, say. It's easier for CX to enforce this rule at least for tickets interlining at their own hub because HK has a looser visa regime for foreigners entering for short stays.