You can just show up and park. You can buy an annual pass directly from the government for ~$100 that covers campsite/entrance fees in pretty much every national park, or put some cash in an envelope with a form and leave it in a dropbox at the lot.

The problem is peak seasons. If you show up to Yellowstone without a reservation on the 4th of July weekend, you'll be lucky if you can even get into the park, much less stay there or appreciate its natural beauty.

So if you want to visit a park during a holiday, school vacation week, or most of the Summer, you need to deal with the bloated mess of a ticketing system which was created by the cheapest new grads that the lowest-bidding rent-seeking leech of a contractor could come up with.

My advice: get used to cold weather and visit in the off season. Nobody is making reservations to hike in Bryce Canyon in the middle of December.