As for a tug that carries the aircraft, son, that has already been done and you should know that this only reduces the life of the landing gear due to the fact that each time you tow an aircraft in that method it counts as a cycle.
Where did you get that kind of information?!? It is absurd!
What you all should realize is that it is not just attaching some dinky motor to the airplane, it is a complete redesign of the wheels themselves! The APU has more power on most aircraft than you would ever believe and that is a fact and as far as I am going to say publicly!
The APU may have plenty of power, but electrical load shedding is already required on MANY airplanes for engine start. In that case, the airplane would have to be stopped when starting the engines, further reducing flexibility of the system.
Also, routing that much electrical capacity to the nosewheel would be a significant wiring feat, further adding to the weight and complexity of the nosegear assembly.