No issues as it pertains to towing on that route, great scenery with mostly light traffic if any. My minor issue is I tow our 10K# 33' TT with a thirsty 3/4 ton Chevy gasser and with the tiny towns you go through on this route it's not like gas stations are abundant by any means.
For diesel trucks not much of an issue with better mpg and larger tanks, with a gasser keep an eye on your fuel gauge. We often tow long stretches throughout the four corner states where refueling opportunities are scarce and have become accustomed to carrying an extra 5 gallons in the truck bed.