Why does the B737NG need electrical power for aircraft towing?
You need power for lighting, fans, intercom, and CVR/flight recorder, cameras; any and all of them are required for towing an aircraft, depending upon its size, and in the event of an accident.

See:


"Aircraft Towing":

Accidents and Incidents



  "B763, Luton UK, 2005 (On 16 February 2005, at Luton Airport, a Boeing B767-300 collided with the tug pulling it forward when the shear pin of the unserviceable tow bar being used to pull the aircraft broke. The aircraft ran onto the tug when the ground crew stopped the tug suddenly. As result of the collision with the tug the aircraft fuselage and landing gear was damaged.)"


  "JS41, Birmingham UK, 2007 (On 26 June 2007, at Birmingham Airport UK, a BAe Jetstream 41 started an engine running pushback without using intercom between ground crew and flight crew. The pushback could not be completed as the towbar could not be disconnected and confusion over a decision to return the aircraft to the gate resulted in an attempt to do so with the aircraft brakes selected which caused the aircraft nose landing gear to collapse.)"


"Pushback":



  "The responsibilities of the ground crew team carrying out a pushback include ensuring that no part of the aircraft structure will impact any fixed object or other aircraft and may include giving clearance to start one or more engines just before, during or immediately after a pushback. The number of people assigned to a ground crew team for a pushback may vary according to aircraft size, but in most cases will be at least three. One will be driving the pushback vehicle, one will be walking in the vicinity of one of the aircraft wingtips and looking beyond the aircraft tail and one will be in charge of the manoeuvre and in communication with the person with aircraft responsibility in the flight deck. Communication between the ground crew supervisor is usually by means of a plug in to an aircraft ground intercom circuit; if so, this is facilitated by a ground crew microphone which acquires the voice of the user whilst excluding background noise, which if the aircraft engines are running can be considerable. If only two ground crew are used for pushback of a smaller aircraft then it is important that the procedure takes full account of the roles of each ground crewmember and that the person in charge of ground crew communications on the flight deck is aware of the number of ground crew being used and the physical location of the supervisor. ...
  Observations of abnormal circumstances in connection with engine starts or any other matter affecting, or potentially affecting the safety of the aircraft during a pushback are of great importance to those on the flight deck but it is essential that any descriptions of external observations during engine starts are imparted accurately; this may sometimes be demanding using ground intercom but can be extremely difficult with only hand signals available.".  



Accidents and Incidents



  "A332, Karachi Pakistan, 2014 (On 4 October 2014, the fracture of a hydraulic hose during an A330-200 pushback at night at Karachi was followed by dense fumes in the form of hydraulic fluid mist filling the aircraft cabin and flight deck. After some delay, during which a delay in isolating the APU air bleed exacerbated the ingress of fumes, the aircraft was towed back onto stand and an emergency evacuation completed. During the return to stand, a PBE unit malfunctioned and caught fire when one of the cabin crew attempted to use it which prevented use of the exit adjacent to it for evacuation.)
  ...


  "B738 / B738, Toronto Canada, 2018 (On 5 January 2018, an out of service Boeing 737-800 was pushed back at night into collision with an in-service Boeing 737-800 waiting on the taxiway for a marshaller to arrive and direct it onto the adjacent terminal gate. The first aircraft’s tail collided with the second aircraft’s right wing and a fire started. The evacuation of the second aircraft was delayed by non-availability of cabin emergency lighting. The Investigation attributed the collision to failure of the apron controller and pushback crew to follow documented procedures or take reasonable care to ensure that it was safe to begin the pushback.)"




There are additional examples available at those links which were not quoted. Sometimes there are external cameras which are useful to record towing operations in the event of an accident.