I towed a 7000-lb trailer with a half-ton Suburban. I broke stuff. The rear axle. Several times. While on vacation.
The weak link in these half-tons is the rear axle. It's, frankly, just weak. It doesn't like to be at max load, and it gets hot if you're on a long trip.
Are you going to be towing 60 miles up to the lake? Go for it. Or are you talking about cross-country road trips? That would be a big "no."
Unlike a pickup, the SUVs have a lot more weight on the rear axle - lots more body and glass. This in turn ends up overloading the rear axle before you get anywhere near the vehicle's "tow rating." Don't forget, people, pets and gear also add to the rear axle weight.
Look for "half-ton towable" trailers. They'll be light enough that you'll be less likely to overload that rear axle. Personally, I'm less concerned about the length, because there are hitch setups like the Hensley Arrow that eliminate sway, as opposed to a simple friction sway brake.
Last thing - more tongue weight means more stability and less sway. Of course, that runs completely afoul of trying to keep from overloading that rear axle. So it's a bit of a tightrope walk. The main reason I upgraded to my 2500 is because the rear axle can carry DOUBLE the weight of the half-ton trucks. As opposed to being the WEAKEST link on the half-tons, the rear axle is the STRONGEST part of the 2500 powertrain.