some company basically owns the rights to do that…?

Usually it's the federal park service (government agency) that runs the parks, and they're the ones that take payment. It's not for-profit, and the fees don't completely pay for maintenance of the park in most cases, they just offset the cost of so many people going (mostly tourists).

And there's usually only one or two roads going to the parks (Yellowstone has 3 IIRC), and they're usually really out of the way, so you're not going to be able to just walk there. Many parks don't connect the entrances either, so they're purely a destination. My brother lives right outside Glacier National Park, and it's still a good 20 miles from the "city" (Columbia Falls is ~5k people) to the park entrance (again, there are two, one at each end of the park).

Yes, these places are massive, but they're also really far from normal traffic, so you'd have go at least a half hour out of the way to get there (often multiple hours driving). Someone needs to pay for maintenance of the infrastructure to get there, and that's what these fees are for.

Sometimes it's as low as $2 or so, sometimes it's like $50 (for more popular parks). It gets adjusted to preserve access for those that really want to visit and prevent abuse. Sometimes it's just a suggested donation.