I'm not sure where you get your ideas of half-empty flights from. BA have the lion's share of Heathrow slots and they're running at something like 86% load factor, so a long way off your idea of Heathrow ops running "half-empty".
Heathrow's third runway will actually be hugely beneficial in terms of re-instating proper competition. BA currently have dominance over slots at Heathrow, so the arrival of the third runway will actually even out the playing field. The third runway will provide more opportunities to the other airlines, and it might even force BA to stop the era of Cruz-ification and refocus on customer service and stop turning its product into another LCC.