Yellowstone really isn't a place to go to if you want to avoid queues of traffic on the main roads. Cyclists can move over and let people pass, but bison herds frequently jam the road as well. Bison aren't terribly likely to understand these sorts of rules. :) (Last time I was there, I occasionally heard a honk during a "bison jam". That did not help anything.)
National parks (at least in the US) have a semi-contradictory purpose of preserving the land for future generations and provide for the enjoyment of the same. Yellowstone is a very crowded park, but the good news is that it's only the "big landmarks" that tend to be this way; most of Yellowstone is not directly accessible by road. All of the day hikes my wife and I did (eg Fairy Falls, Mount Washburn, etc.) were not terribly crowded at all. I can imagine backpackers actually getting some serious solitude.
I don't see a need to go as drastic as "ban all ICE vehicles" because keeping some things very accessible fits the public interest of enjoyment. It would be interesting to explore the idea of more cycling paths in parks, because cyclists are relatively low impact, and my perception of Yellowstone was that the number of long cycling-friendly trails was fairly low.