I'm sure that intercontinental airlines would move all operations from NRT to HND if there were no restrictions on operating hours. As it is I believe that intercontinental flights cannot operate between 0630 & 2230 local (happy to be corrected if wrong). The current BA schedule is:
LHR 0805 X23
HND 0455 X34
HND 0625 X34
LHR 1000 X34
This might work for First/Club the idea being that you arrive at 0455 after a night in your sleeper seat ready for a days work and after a long days work. I would certainly prefer NRT for a leisure trip. Yes its in the middle of nowhere but at least the times are civilised.
Airlines would generally prefer a night flight and JL operate a codeshare with AF to the following schedule:
HND 0130
CDG 0620
CDG 1100
HND 0655
BA could utilise the slot currently used by BA212 to give the following schedule:
LHR 0935
HND 0625
HND 0140
LHR 0515.
This would mean a plane on the ground for 19 hours although with 747s in the Nevada desert this might not be a problem - except that the 747 may be too large an aircraft.
Alternatively JL could operate the route and BA increase frequencies to NRT if they are given authority to codeshare.