Having had the misforture (fueled by stupidity) of trying to cut across grass in a TAA Toyota tug after towing a Cessna that collaped nose gear at Wynyard, and subsequently sinking to the axles and need the fireys to drag me out, I can understand why QF did not offer a tug to do the job.
The main problem is the extra weight added to the vehicle to allow effective braking with the weight of an aeroplane behind it.
The toyota tug was rated up to DC9, and the rear was solid cast iron. QF Hobart (or whatever brand they are now) tugs would be similar I am sure.
Best
EWL