Or, in the case of Auto-Train, they pushed into an unwise expansion and then had those derailments.Correlation ≠ causation. Battleaxe tried to privatize everything but strategic sheep islands, private companies left infrastructure to rot to untenable levels, and then the government had to re-nationalize the upkeep again. It has taken decades of effort and many billions to fix what the privatization hath wrought.
When I looked at what actually happened to many private passenger rail companies it was often a severe external setback (like the the 70's oil crisis, the 80's savings and loan implosion, the 90's dot com bubble, the 2001 travel collapse, the 2008 mortgage default, the 2020 pandemic, etc.) that did them in. The core idea seems to have a market with willing customers, but either does not make enough or does not save enough to survive extended market downturns.
[I strongly suspect that if Auto-Train had stuck to LOR-SFA alone, they might still be operating.]