British Grenadier
Yes, I am familiar with the BA handling operation,(& also the DNATA & Menzies operations), but would have to respond to your, maybe, "tongue in cheek" comments as follows
I think you may have ignored the practicalities of any merging/takeover of BMI flights by BA.
Bear in mind IB went to BA for the ramp work at T3 & they certainly didn't do it for cost saving reasons. They became, with BA, a part of IAG, so BA were effectively handling their own traffic at LHR when they took IB ramp at T3. The same occurs when they either merge or swallow BMI. They have to meet their own in house MCTs for LHR for what is a BA to BA transfer, regardless of the terminal. The politics from above will probably dictate that they have to handle their own traffic, maybe not initially if part of the operation remains in T1,{ As with IB when PH (now DNATA) retained the ramp} but certainly out of T5 & even T3 if part of the operation were to go there.
So, if cost is not the key issue then BA will staff it as they currently do & the pax will see the aircraft depart as previously & for arrivals the bags will come up within target. The difference is that BA will allocate more staff to the operation than PH/DNATA did for IB or Menzies do for BMI. If BA could overcome the cost differentials for the IB handling then the BMI operation, which will become in one form or another, a part of BA, should be no problem. It's a pity we don't get to see the final figures!