Why don't they start a Birmingham - Heathrow route
For most in BHX's catchment it would be quicker to drive to Heathrow than fly via BHX.
Through codeshares, BA serves BHX via Aer Lingus, Iberia, Qatar & Vueling. You can fly almost anywhere in the world from BHX using BA. It's just none of the flights will be on BA aircraft.