Perhaps the key factor that was brought up about that BA decision to continue was that the 744 is in fact certified for continued operation on 3 engines.
It wasn’t based on some general philosophy of 4 engine airplanes, rather that the -400 specifically had sufficient redundancy on the other engines, eg electric sources etc.
As I recall the -100 and -200 were not so certified but the -400 was (not sure on the -300).
(This is based on pprune members at the time, can’t personally confirm it).
For this flight it sounds like there can be no concerns as to not being certain of cause of the engine out. Some brought that up for BA although I seem to recall the report fully exonerating that aspect.