If you have no choice but to pay the ‘fee’ (as in your scenario) it is indeed a tax. However, if you have the choice whether or not to use a service, the ‘user fee’ is not a tax. It’s just the cost of something you wanted. OTOH, you’re forced to pay a tax, whether or not you want any government services.
If they ever took a dime in taxes then everything they take is taxes regardless of spelling.
You are absolutely right and user fees are the very fairest way to raise revenue. They are NOT a tax in the way we speak of taxes today (income tax).