Gawd, I hate driving. I'd never consider driving that. I can manage not more than about three hours in a car and then I want OUT OUT OUT.
Yes, it's beautiful country, but I wouldn't do it unless I was going to be intentional and stopping along the way to see the sights. Actually, after looking at the map, I'm not sure there are a lot of sights to see. St. George is the most Gawd forsaken place I've ever been. Driving through southern Wyoming isn't so great either. Just my opinion.
Fly.