RVs are a great way to travel. The TripAdvisor people are dead wrong there, in my opinion. Particularly with a large group, I would much, much rather be in a motorhome than in a minivan when going down the road. (I will admit that, in the event of a serious crash, I would much prefer to be in the minivan than in a motorhome...but naturally my goal is to avoid being in a serious crash in any case!)
As others have said, this is an extremely aggressive itinerary, maybe even an impossibly aggressive one. The west is big and spread out. You'd almost certainly be spending more time seeing the inside of your RV than the parks you're intending to visit. I think the idea of only doing the southern parks (or perhaps only the northern ones) is excellent.
There are a few people here who apparently don't know or recall what it was like to have limited vacation time available, and wouldn't dream of spending less than an entire summer to see the parks you list. That's frankly absurd for most families or full-time employees; and while having a lot of time is undoubtedly grand, it doesn't hold that those with less time should never go anywhere because it's too rushed. Still, there does come a point where it's hardly worth the effort to travel a very long distance to see a destination for only a couple hours.