An APU uses a fraction of the fuel used by main engines. The weight of the system is no more than the weight of 'taxi' in fuel thus not required to be loaded & carried during flight.
The WheelTug system design is one of low maintenance. Another WheelTug bonus is reduced maintenance on those components consequentially used less; Engines & Brakes (Carbon brakes wear badly when cold). Also of note is the reduction of engine FOD damage which progressively reduces fuel efficiency in flight.
The ground crew is (typically) 3 instead of 4 people, who would converse with the pilot as they do now. With the (infrequent) occurrence of an engine start problem, return to gate.