Just to be clear, you CAN pick any US location you want. You can NOT be taxed on a boat that's not in that state.
However, the tax bureaucrats in many states have learned to scan the documented vessel database for any hailing ports
in their state. They'll send a tax bill to each owner they find. It's not their job to confirm the boat is in the state, just to send the bill.
Once the tax bill is in the system, the wheels of another part of the bureaucracy start turning. If they don't receive payment, collection action will eventually begin.
Collection isn't a criminal process, so there's no concept
of "innocent until proven guilty." Anyone can claim you owe them money
, and it's up to you to prove you don't.
You would win in the end, but is it worth it? Just pick a hailing port in a no-tax state and be done with it.