You are correct average turnaround at LHR is 4 hours plus. Other conditions govern usage as well e.g. time of arrival / departures from LHR or to LHR. Pax are not happy leaving home on a longhaul flight in the early hours. Likewise ex UK pax do not wish to travel longhaul at 07;00 hours. Then consideration is given to arrival times and turaround at the destinations.
Your other point is indeed that at this time many airlines and the aircraft are not making money as the yields / ASK (actual seat cost per kilometer) are not high enough to make profits (desired). At BA I know we have parked up 3 or 4 747's at CWL and maybe one is parked but rotated week about at LHR. Finally BA intends to reduce the summer programme by at least 2% and reduce the Club Europe numbers by seat change plan. Hope this has answered a couple of your points.
Finally in the long term I expect you will see twin engined aircraft (777 / 787 / 350 / 330 ) replace many of the 747 / 340 aircraft which will be grounded to save cost the only exception the 380.