To answer the OP, I would say it is doable, but not pleasant. A lot of hard driving time. But doable. I've driven from my home (which is on the shortest route between Grand Canyon and Yellowstone.) to Grand Canyon. We left my home about 8:00 AM and arrived at the rim of Havasupai at about dark. Granted, we stopped to visit family in Southern Utah, and stopped for a nice dinner in Arizona. Plus, we accidentally took a small detour. But it was a long drive. I've also went from my home to Yellowstone. It is short of 6 hours. So for me, I would not try to drive that entire route in one day.
As mentioned by others, interstate in rural Utah is posted at 80 mph. It isn't accurate to claim that traffic flows at 90, however. More like 82 - 83 mph. It is safe to do 5 over without getting pulled over. You can do up to 10 over in other speed zones on Utah interstate.
You didn't say if you are shooting for the West gate, or the South gate. West gate is an easier drive, if you want more interstate drive time. South gate is more two lane, but a much prettier of a drive.
As others have mentioned, if it were me I'd plan more time. I know vacation time is limited. But it would be very nice to see Zions, or Arches. If you've already been to the Grand Canyon, Bryce is somewhat more of the same. But it is very nice.
But if that is not an option, I'd still split it up. Perhaps from Grand Canyon to SLC. If you like American history, SLC offers a lot of things to see. Plus, it is pretty city anyway. Tucked right up against the Wasatch mountains. The second day take I-15 North to Brigham City, Utah. Get off the interstate in Brigham City and take Hwy 89 through Sardine Canyon to Logan, Utah. From Logan stay on Hwy 89 through Logan Canyon, which is one of the prettiest drives anywhere. (And I've been in more states than I haven't.) You will come out of Logan Canyon into Bear Lake. Also absolutely beautiful scenery. From there you follow 89 North all the way into the West gate at Yellowstone. Another mandatory stop will be in Jackson Hole, WY. Get your picture under the antler arch. It's one of a kind. In my opinion, this should absolutely be your preferred route.
You won't be disappointed if you take the route through Idaho, up to West Yellowstone, because it is also a pretty drive. And since you will have never seen the other route, you won't know what you missed.
Good luck with your vacation plans. Hope it is everything you are looking forward to.
Originally Posted By: Nick1994
Originally Posted By: Quattro Pete
Originally Posted By: widman
The question would be: Why?
There are half a dozen routes that are the most beautiful in the country. You could easily enjoy a few weeks on that route.
Unlike other countries, vacation time in the US is not seemingly unlimited.
But I agree... sometimes it's about the trip, not about destination.
Back when I was young, we did the whole US (from east to west and back to east) in 4 weeks. Would I do it again? Yes, but not in 4 weeks.
There's also not a lot to see in Utah.
Perhaps you can convince all the tourists that come from all over Europe and Asia to visit Arches, Zions, Bryce, Monument Valley, etc., that there is nothing to see in Utah. Tell them all to spend all of their time in your home state, at the Grand Canyon instead. Then it will be easier for Utah locals to visit these most spectacular parts of Utah.