Certainly BA did this for commercial reasons and while not terribly difficult from an ops position (a 747 can fly with three or even two engines without major difficulty)
The whole airline is run for commercial reasons, like any airline.
The Smart Response would have been to land at JFK and transfer pax onto existing BA flights.
Except all the JFK flights had long since departed, they'd have been trying to find hotels for passengers at 3am Eastern time and the aircraft could have continued to the UK safely.
As it happened the craft had to divert to MAN anyway due to fuel issues. It made, IMO (but just MO, okay), BA seem cheap and penny-pinching, seeming to want to avoid EU compensation rules, et al.
Except compensation wouldn't have been paid for a technical diversion anyway. It's hard to second guess public opinion when they are apt to put two and two together and get seven.
My point was that BA's response at the time was (said in a very 1930s headmaster voice): "Well we're sure the American authorities would have had something to say to us if we dumped all that nasty jet fuel over Huntington Beach so obviously the only sensible thing to do was fly all the way to London", which sounded ludicrous and did little to improve BA's battered public image at the time (sound familiar).
Actually, the response was along the lines of "We have committed no technical violations, we are confident the American authorities will see it our way when they have all the evidence and the flight was perfectly safe to continue". BA were right, the FAA were very, very wrong and there was much red-faced back-pedalling at FAA HQ, starting about 24 hours after their engineers got hold of the technical info and started banging there heads on their desks in despair at what their politician boss had said.
Whereas an overland flight to JFK and transfer to other BA flights and engine maintenance at BA's flight centres there would have gotten the job done without any high drama and theatrics.
LAX to LHR is predominantly overland. The aircraft would have been ferried empty back from JFK on 3 engines to be fixed in London.
Edited to add that if you actually read the first link posted by vla it's actually an excellent defence of the BA crews decision!