Many times, since I lived in Moab and traveled north to, or through SLC. From I70-Helper it is pretty straight a few little hills. From Price to Spanish Forks you start out in a twisty little canyon and then slowly drive up to Soldiers Summit (7764 feet), then back down through some more canyons and then into Spanish Fork and I-15.
Helper UT is at 5800 feet, so the climb, is not bad and after cresting the summit you are entering the great basin area (Spanish Fork is 4570 feet).
Going south to north, it is one lane over the summit, but if coming north to south it is two lanes.
Canyons can get a bit windy at times; just traveled it a few weeks ago and yes, there was a lot of swaying from big rigs and larger trailers. But thousands of trailers do it weekly at least. It is a very well used shortcut to SLC from I70.
Only other option is stay on I70 to Salina then take Rte 50 over to I15 and north into SLC. I have traveled this route a few times and it adds about an hour to the trip; that is unless you stop at all the San Rafael Swell viewing locations; then add another half-hour to the trip; easily.
Both are quite scenic in places; but the swell is really beautiful.
Trailer: Lifted 228BH, heavy duty springs and Yokohama tires
TV: 2016 GMC Sierra Z71 4x4 CC, SLT
Spare TV: Two Alaskan Malamutes
Living somewhere in ID; previously lived in Moab UT; previous to that, don't ask!