The location and identity of all aircraft in the US is public information. Just like posting the home address of the US president isn't doxxing either.
Disagree--it's quite possible to fly a plane from A to B without it being public information.
However, to operate above 18,000' you have to cooperate with ATC and it becomes public. Likewise, to operate in the airspace near any major airport (pretty much, to operate in/near any big city) you have to cooperate with ATC and it becomes public. Out in the middle of nowhere and below 18,000' those rules don't apply, so long as the air is clear enough for visual rules operation you can simply fly somewhere without talking to anyone. It's not the best idea but it's legal.