A tow bar has shear pins to prevent too much force being applied on the gear during a tow. Is a tow crew (by regulation) allowed to pull aircraft off grass or are they not even allowed to try? If allowed to try, what stopped the aircraft moving? Shear pins breaking or tug wheel traction?
Well if it's a steep/sharp drop off your tyres might be damaged for a start.
I'm sure tyres can survive a small drop off a ledge if they can withstand landing forces. The main concern would be fore-aft strains on nose gear (strut assemblies, etc) if being towed or fore-aft strains on the main gear if being powered out.