My brother and I just did this very thing last week for a mule deer hunt in Colorado . We are both in Ohio. In the past, we have flown for hunting trips to Wyoming and New Mexico. We rented a Tahoe and it was a nice vehicle. Very roomy, comfortable and smooth to drive. We had plenty of room for coolers, gear, etc. It made hauling two muleys back very easy.
While it certainly takes longer than flying, it is lessened when you add in the trip to the airport, security and check-in, flight time, connections, picking up a rental car at the destination airport and then a drive to the actual hunting site. For us, it takes an hour drive to get to the local airport in Ohio and we would have had a 4 hour drive to the hunting site from Denver. The total drive was 17 hours and we did it on our schedule, not the airlines.
I looked at the drive as part of the adventure. It kind of felt like I was back in college (which sadly was 25 years ago). We got to see new country or revisit areas we hadn't seen in years. We also had plenty of time to talk and "hang out". Having the vehicle with us also gave us flexibility to run some errands and take care of details after we harvested our animals and before we headed for home.
I do suggest getting a big vehicle to make it worth your while on multiple fronts (including leg room for pulling over to catch some sleep as needed). Having satellite radio is paramount in my opinion because it adds so much entertainment value for sporting events, talk radio, consistent music of any genre. Finally, I do suggest paying for the insurance coverage if your personal insurance does not cover a rental vehicle. Factor that as part of the trip expense and it's better than ruining a trip due to some cosmetic issue with the vehicle.
Based on our experience, unless it's for something further west than Wyoming/Colorado/New Mexico, I don't think we'll fly again for a big game trip.