A lot of Boeing aircraft now do have FBW, certainly the 777 and 787 do. Essentially the computers can fly the aircraft more accurately than a human, which is more fuel efficient. Part of this is down to reducing the stability of the aircraft which means there's less drag as your control surfaces aren't working as hard to keep it pointing in the direction you want, although they are moving more often. It would be very tiring for a human to fly an aircraft with reduced stability hence the FBW. Although you'd still get fuel savings with the autopilot flying a positively stable aircraft because they're consistently better over a long period of time.
And good luck trying to sell a less fuel efficient aircraft to an airline.