I've towed with a Tahoe for years. No major issues. A little sway with high winds or passing trucks, but that can be remedied with a better WDH system. Otherwise, we've put at least 15,000 miles on two Tahoes towing over the last 7 years with two diff't trailers.
The main issue to watch out for is overloading your payload capacity depending on how much stuff you put in your truck. I just put people and dogs in the truck and the rest of the stuff in the trailer to keep the payload down. We pretty much tow at capacity, but thats what it's made to do.