>>901934National Parks are heavily regulated with the purpose of preservation. The point is to leave the land as undisturbed as possible and limit the destruction that comes from human interaction with the land. Sure, sure, we'd never trash the place, but millions of shitty humans going off trail will bring ruin to the parks.
Go visit, but remember National Parks are more like a living museum, designed to display and present. Camping it very limited, contained, and frankly disappointing if you're looking for wilderness.
That being said, most western National Parks are surrounded by National Forest, Bureau of Land Managemet, National Wilderness and various state conservation lands which are usually much more lax in terms of use. As stated National Forests allow hunting, fishing, resource collection, dispersed camping, etc.
Also remember, National Parks are created by congress and are usually considered to be sites of such importance that they need to be preserved for the ENTIRE nation. That means they need to be so important that CONGRESS need to AGREE that they are so important they need to be taken away from states and given federal jurisdiction. Good luck getting congress to agree to just about anything.
If you're going to Yellowstone I suggest Shoshone National Forest. Its very large, very beautiful, very easy to access and just as beautiful as anything Yellowstone has regarding the high country. Stay there and drive into the park for the day and then come back.
Also, you DO know that Yellowstone and Yosemite are about a thousand miles apart, right? You'd be surprised how often people misjudge distance and time in the west. When I worked in South Dakota people would tell me they are going to head to Yellowstone later that day. They don't realize it takes 8 hours to drive from Rapid City to Yellowstone when you factor in stops, food, and sightseeing.