Fully agree. In a civilized modern country the government would own the rails (because, I mean obviously it would) and operators would put out timetables and requests for trains - all managed by the government. Just like the UK and most other countries, the government is in charge of maintaining the rails, keeping them safe, and expansion, while the operators do what they do best - they manage their schedules and try to squeeze the most profit out of it.
It’s a win-win, private industry doesn’t have to worry about safety or maintenance beyond their own vehicles, they work with the government on scheduling, and passenger rail would get a resurgence because adding new train lines and stops would just be a matter of starting a new operator.
If you thought of a new commuter line that you think would benefit a region, it wouldn’t be trying to convince Amtrak to do it - you could literally raise the money and start your own operator, lease some vehicles, and then literally just start running your train line operated on government tracks. Just as the semis do on the interstate system, just like airlines do.