Higher mileage Jeeps are also know for the "Jeep death shake/weave" on their own, even without a trailer. Not a good choice unless worn suspension bits are replaced.
Yes, we owned a 1998 Cherokee Sport for a couple years, lots of bottom bits were replaced.
High CG, tall tires, worn bits, shortish wheel base for its height.

A good tow vehicle should be sorta heavy, long, low (think 60's & 70's US station wagons). Yes, other vehicles can tow (I crewed, about 1979, driving a VW Beetle towing a plywood ASW-15 trailer, it had a hard time doing 55MPH on flat ground.....empty!), but some vehicles have an easier time with ANY trailer.