I understand why people would prefer user fees to nationally-distributed taxes. What rubs me the wrong way is the lottery application fees. Charging the people who visit a park is one thing. Charging people who want to visit a park, apply to do so on a govt website, and are denied, is another. If this was an account setup fee I might be able to understand. But charging it every time you throw your hat in the ring seems inefficient and exploitative.
It's probably an effective way to prevent bots (or even humans) from spamming the lottery if entry to the lottery was free or gated by a one-off fee. The exploitative part is mostly that these per-application fees are pocketed by a private company.