It is hard to believe that this simple concept seems to be lost on so many... not the OP in particular, but the majority, in general.
Not pertaining to rough ride but to knowing how tire pressure affects a vehicles ride and handling....
I did it again, in Dallas during that snow a couple weeks ago. We stopped to help push a guys suv up a hill , stuck at an intersection on a slight incline.
Was too slick for me and the 2 kids w me to get any traction as well, so I let a bunch of air out of his back tires (clueless jack wad didn’t even get out and help, or get out and stop me from doing it) and off he went. No push needed!
Drove a rear wheel drive sedan 650 miles , mostly through a blizzard to get out of Dallas. First thing I did when I filled up w gas is dropped the tire pressure to about 25psi all 4 tires. That car scooter through the snow and tracked like a one horse open sleigh!