I think the basic driver on the number of engines on an aircraft is simply financial.
There are all kinds of arguments being put forward about safety, ETOPS, take-off parameters etc., but surely the aircraft manufacturer will provide an aircraft that can comply with the requirements at least cost and lowest running costs.
It is naturally possible to expand the argument in all sorts of directions but to cut to basics, two engines will cost less than four, they will be more efficient and therefore use less fuel.
Do you suppose that the Airbus A380 would have two engines if there were large enough power units available? I think it quite possible, if the Certification Specifications could be met.