I don't recall anyone saying that they should.
BA typically have about 70 aircraft (roughly a quarter of their fleet) on the ground at LHR overnight (not including aircraft in the hangars).
It won't come as any surprise that the number swells to just under 100 by around 0700, with both the early-morning longhaul arrivals and the first shorthaul inbounds mainly from European countries on CET.
From about 0800 the population stays pretty consistently in the 80-90 range until the late afternoon, after which it gradually declines to the overnight figure as aircraft depart for night stops abroad.
Obviously the count of aircraft on the ground at any point in time includes aircraft taxying in/out, holding for takeoff and being towed to/from the Engineering Base, so actual stand occupancy will be a correspondingly lower figure.
I am at Heathrow most days throughout the year and cannot understand that T5 is apparently at capacity. However during the Summer season Charters are given T5 capacity. As there seems to be no ryhme or reason to the T3 flights. IE aircraft type, or country of origin. One would think Charters could not be accomodated at the "Flagship" terminal. Just curious?