I apologize for being unintentionally vague on what privatization would look like for the NEC.
Why should the NEC become privatized?
Your second paragraph contains the answer (edited):
... the NEC is the one place in the country where passenger rail is a significant part of the transportation system. Also, both Washington and Wall Street movers and shakers ride the service and thousands of their employees use it to commute to work or travel for business,
That seems like a captive audience situation where the alternatives are, at best, not great. Someone, somewhere would take a look at the math and determine if some sort of NEC operation could pencil out some profit extraction.
Now, do I believe Amtrak would just sell the whole NEC (rolling stock, land, bridges, tunnels, etc) to one person or group? That's
very unlikely. That would either take some crazy dealing by the Feds, someone who has Berkshire Hathaway, Jeff Bezos or Elon Musk money, or both. (If Elon Musk bought the entire NEC as-is... well, all bets are off about what the NEC would look like.) More likely, the privatization model would look like what the UK attempted before their latest report abandoning the scheme.
The land, non-rail infrastructure (bridges, tunnels), and stations would return to the individual states "in the public interest" to keep commuter rail running. I don't think that would change much, except perhaps how infrastructure projects get funded later on. Some rejiggering of Federal money to/from the states would likely happen in exchange for the land transfer, so the states aren't completely holding the long-term financial bag for Amtrak's collapse.
The operations/rail infrastructure side (e.g. track maintenance, signals, overhead wire work, dispatch) would probably go to an organization similar to Network Rail in the UK. I could see the Feds running this part for a while and just charging the states the cost of doing business, handing it off to a "joint powers board" corporation owned by the states to run it, or handing it over to Conrail Shared Assets. Handing this off to a single Class I would be ... scary, which is why Conrail Shared Assets exists today.
The rolling stock and actual above-rail operations would likely be the fully privatized bit, and the thing people associate as privatization. Whether or not it's open access (like Regiojet/Flixtrain) or if it's one operator like Arriva/DB being contracted to run the NEC on behalf of the states is another matter, determined by legislation.