I think that's exactly the way BA should do it and in fairness they already do generally speaking, where the summer sun/winter ski flights go from Gatwick and the domestic and international cities and worldwide hubs are served from Heathrow.
There should be a really clear and distinct difference in the type of travel market they aim to attract at Heathrow and Gatwick and should be less competition between them and very few routes that go from both. I'd say get rid of the Scottish routes from Gatwick and maybe some of the cities like Amsterdam, Barcelona and Rome and fly them on bigger aircraft from Heathrow and allow more space for summer sun/winter ski routes from Gatwick. At the end of the day, the traveller who wants a full service flight between two cities will prefer Heathrow and for a low cost flights would prefer Stansted or Luton, Gatwick is a bit in the middle and maybe better for the holiday flights, plus that's what Gatwick is traditionally known for.