The towing capacities that manufacturers give trucks, particular “half-tons” aren’t really applicable in real life. You’ll run out payload capacity well before you run out towing capacity much of the time. For example the 2021 Silverado, in it’s most popular configuration (4WD, Crew Cab, Short bed) has max payload capacity of 2060 pounds. With the 6.2L gas V8 it’s rated for 11,900 pounds. However you want at least 10%, but no more than 15% of the trailer weight on the hitch. This weight gets transferred to truck. We’ll split the difference and go with 12.5%. So, at this point you transferring about 1500 pounds to the truck before you sit down in the driver’s seat. You effectively have 560 pounds of payload left before you start. If you’re bringing a family of 4, you’re over the payload limit, if you’re only bringing two people, (let’s say 350 pounds), that means that, you’re going to be limited to about 200 pounds for food/luggage/supplies or whatever. That’s that’s not giving yourself a 10% safety buffer or anything. It’s not a very realistic towing capacity.
The real-world practical limit for most half-ton trucks is going to be around 7,000-8000 pounds. That gives you a lot more leeway in terms of payload capacity.