It's one thing to cross the open spaces of Utah without using freeways, and quite another to pass through a major city using the surface streets.
The fastest route Google Maps gives me bypasses most the the SLC area by taking I84 to I80 (just a bit of Ogden). Later it passes through Denver, and Dallas.
If I tell it to skip 'highways' (ie freeways), it adds about 5 hrs to the drive, and avoids even those cities. A non-freeway route through a major city will not be fastest. The non-freeway route through Oregon and Nevada to NM looks interesting, using roads like US95 and 93. It even avoids the Colorado mountains, though the use of UT14 east of Cedar City UT is a bit questionable (for RVs).
Choosing a route across the plains east of the Rockies (I25) is quite different from choosing one across the semi-desert of eastern OR, NV and UT, and th across the Rockies.