The short answer is that national parks are not a self-contained business, they are held in trust for all Americans. Very high entry fees would violate that trust by excluding most citizens. So they are primarily supported by taxes, as they should be.
Parks do generate a ton of economic activity, but directly capture little of it. Airfare, gas, lodging, meals, retail sales, social media revenue, etc. mostly happen outside the parks. Like the highway system or national defense, they are a national platform that is federally maintained.
All that said, a national park is fundamentally not an economic concept. It satisfies a national desire that is deeper than just making a bit of money. The economic story is just another way of saying that tons of people love the parks.