The problem is always one of liability. Concerns about insurance coverage. Compounded by tires, brakes, wheel bearing service, then proper lamp performance (clearance, stop & turn signal) as well as safety chains, breakaway switch and the cord/plug that connects to the tow vehicle. The TV brake controller and proper tow mirrors. Not to mention a proper hitch and hitch receiver. Some knowledge of how to set that up.
It's a fair list, in other words, that needs familiarity.
I can see the concern by the PO via a quick map consultation of the route. Payson is at about 5,000/ft altitude and Phoenix at 1,200/ft. The connecting highway -- AZ-87, The Beeline Highway
-- has the usual "sharp" turns of a road in ascent or descent along the route. But it is four lanes according to the Wiki link (late 1990s/early 2000's) and I see no truck restrictions.
I haven't been up that road since about 1970 (the route my grandparents used to take from Mesa to Show Low). A drive in a 1971 Chrysler (then new) that became mine some twenty-four years later.
GMaps sez about 76-miles.
A four lane with a decent shoulder (width) would keep what -- for me -- would be the worst part of such a trip from being scary: lane width and shoulder width . . it's easy to let the tail of a travel trailer stray into the adjoining lane. But that road may not have much in the way of "shoulder" (as we expect on an Interstate). A low-traffic morning and keeping to the right side of the lane (which I'd never otherwise recommend) would -- with above issues answered -- keep any troubles to a minimum.