I've towed with minivans for decades (Toyota and Ford, not Chrysler). Never had to replace a transmission, or any other part related to towing, and keep my cars for at least 10 years and generally put well over 200K miles on them. The Ford had a new Rack&Pinion put in at 120K miles, a common issue for the older Windstar, unrelated to towing. Never had an issue with using WDH (in fact, they're recommended by both Ford and Toyota) and never had an issue due to having a high wall trailer. IMO, most of the opinions to the contrary are likely from people that just haven't done it.
Advice:
Stay within your vehicles weight ratings and they work just fine, and are in fact very stable tow vehicles. Very low center of gravity, long wheelbase.
Use a quality WDH with sway control.
Weights to check and verify (at a scale, fully loaded for a trip, including passengers and cargo): Individual axles for axle weight, total axle weight vs. tire ratings, hitch weight (with a tongue scale).
Don't tow with a full water tank. That water adds several hundred pounds.
Tow at 60mph on the flats.
Learn how to pull long grades. (Figure out where your engine's power band is. When going up, put the engine in the power band (a particular RPM range) and keep it there, letting it downshift as necessary, and don't worry about speed as you down shift and slow down. Keep it in the power band, and you'll end up passing much larger tow vehicles that don't know how to do this. Going down, manually downshift as much as your vehicle will allow to use the engine for braking. Periodically brake firmly to slow down to 45-50 mph, then let the car coast with the engine in as low a gear as it'll do to control speed, until it gets up to about 65, then brake again ... Doing this will allow you to not have to brake too often and keep from overheating the brakes.)