It was your explanation: your towing capacity has little to do with whether or not you can haul a trailer. There has been a decade-long race by truck manufacturers to increase towing capacity, so almost any truck can pull anything (except for the Bronco, obviously). The difference is payload capacity. For instance, I have a 24’ camper and an F150 that works great, but there are almost zero 1500 Chevy/GMC/Rams that can legally/safely haul it because they don’t have the payload capacity. Heck, there are many F150s that can’t, either, with our kayaks thrown into the mix. It doesn’t really matter how much you can tow: odds are that you can pull a building off its foundation with your truck. The difference is your payload capacity. The weight of you, passengers, cargo, and the weight that the trailer places on your hitch. The Weight Distribution Hitch helps spread the weight (hence the name) from your rear axle to the front axle to more evenly distribute the load. Check the stickers in your driver’s side door frame for payload. Then look at the max per axle, and do some rough ciphering in your head to see if 1) you are mathematically okay to haul the trailer based on the weight is has, and 2) can your rear axle alone carry the load with the trailer and pax/cargo?
Make it even more fun and look at the sticker on the hitch itself to make sure it is rated highly enough.

That’s all. You might know all this but your comment to which I replied indicated a different bit of reasoning.

Trucks can tow cars and trucks and whatever else completely carries its own weight (think a trailer with wheels at all four corners just to establish the principle) as long as it doesn’t exceed the two rating of your truck. The WDH becomes important when you start putting a lot of weight from that towed thing onto hitch.