Bid_time,
If you look at the recent about 5-10 yrs ago, towing specs put out by ASE group, nowhere is it assumed that tire capacity per say is a limiting factor of one's tow rating. It;s generally speaking a performance factor. Acceleration, holding mph above 35 or 40 mph depending upon the total GCW of the vehicle in 100F temps on a 5% grade, NOT overheating mechanicals! Starting on in forward and reverse X times on a 12% grade and not overheating the mechanicals or brake fade. Ebrake holding gcw on an x% grade. Yes, you do need payload for the HW of the trailer plus # of occupant's times seatbelts at 150lbs per person. SOme cases, a 5W will be lower rated than a ball mount. a 10K trailer will need generally 10% or 1000 lbs to 15% 1500 lbs, vs a 5W at 2000-2500 lbs of HW for the 10K lb total weight trailer. If you only have 2000 lbs of payload, 3 seat belts, max trailer is around 10K in a ball or pintle hitch setup. A 5W is generally speaking out of the equation.
Payload is the only real place tire capacity comes into play. As I noted, if tire capacity, axle, springs etc are too low for the payload needed, you have too small of the vehicle! doesn't matter if you are or are not towing.
At the end of the day, if you do not have the payload needed for the HW of the trailer, you have no trailer tow capacity!
Marty