Selling it to private owners is a good idea. If it had been privately owned they wouldn’t have been in this predicament. I bet the public employees unions are adamantly opposed to this. If it was sold they will demand the new owners keep the union workers.
It was privately owned, Penn Central went bankrupt remember. No private company would take the corridor without at least getting the money that Amtrak is already getting. And I don’t know of any public unions involved in the station except a few TSA.
Last time I checked, airlines had unions too.
The problem is that a lot of people in the northeast rely on the rail network but it doesn’t make enough money to cover its infrastructure cost. (airlines don’t pay for airports, and the gas tax doesn’t cover the roads but we won’t go there). New York would shut down without the railroad so losing it isn’t an option.