Amtrak has from the start been a weird mix of public & private. As much of a small government person as I am, I do realize that it isn't sustainable as both and needs to be one or the other. I personally favor private, as there is very little that the government does better that the private sector. I am impressed to see what Brightline accomplishes, as the prevailing wisdom was that private passenger service was not a good business. The government need not concern itself with profits and instead could simply put trains where t thinks they are needed. On the one hand that is a plus, but on the other if there is not profit potential it probably means there isn't much need.
Years ago, during the debates on public healthcare, I saw a comedian doing a routine. He brought up public housing projects. His joke (which a good joke always has an element of truth in it) was that if you wouldn't live in public housing why would you seek treatment in a public hospital? The same could be said about public trains. Flex dining, dated interiors and chronic lateness are all symptoms of this.
Not that long ago NYC used a mix of public and private busses, with private companies running regular routes. They changed to an all-MTA bus system. Oddly enough to circle back to health care they have a three-tiered ambulance system. I think there is room for both public and private trains, but probably not in the same entity.