Both of my trucks have "P" tires on them, the blue truck had Goodyear Wrangler RT/S tires...
I have never felt comfortable hauling a trailer with that truck.
That being said I've done it many, many times. Inevitably in life you do things occasionally that you wish you didn't. I've laid awake at night before long trips and worried about all things in general about the trip. Whether the truck will make it. If I will loose an axle bearing on the trailer. On and on... The tires always worried me. Always.
I've never had a blow out with the "P" rated tire. I've blown the tread on at least 4 "E" rated LT tires. (three coopers and one uniroyal)
Right now I've got them on the black truck. They ride really nice and smooth. I haul nothing whatsoever with this truck.
If you are at a point where you are buying new tires, by all means get the higher rated ones. I would have had fewer sleepless nights had I bit the bullet a year ago and bought the blue truck the right tires...
Just because you can do something doesn't mean you should. Just because something hasn't happened before doesn't mean it won't...