Just seen LAX LHRs edit. Clearly the obvious reason would be lack of space at peak times! LBA is very short of apron space these days! In particular wide body stands are at a premium.
Exactly. Aircraft are being parked on a closed taxiway during the night as it is. Whilst its mainly peak morning times LBA struggles, its often the peak time for diverts should there be fog/overnight snow etc.
Also, whilst LBA *used* to handle B747's, it would likely struggle now given the space (the B747's used to park parallel to the terminal IIRC and thus take up 2-3 stands) and such.