BHX is just one of a number of airports that needs a link to LHR for exactly the reasons you mention
I don't agree that BHX need a domestic flight to LHR. If you want to get to london, you use the train. If you want to go further afield you fly to via a European hub. Most of them are immeasurably a better passenger experience (even Frankfurt!) than LHR.
If BA were interested in Midlander's business then they would consider operating from the Midlands directly to European, and a handful of worldwide destinations - but given their decision to hand the BHX network to FlyBe they clearly ain't! Same can be said for Manchester!
we have a captive market - they'll all go to LHR anyway
If BA/IAG think this then they are living in la-la land. Star Alliance and Skyteam shifting so many thousands of passengers via continental hubs lays that bare to the nonsense it is.