I guess the airlines and freight railroads, which are private but have unloaded virtually all their infrastructure costs onto various government, are doing their best.When you have a profit to defend, you tend to do your best. Any government funding they've received have been in the form of bonds or tax breaks. If you define those as making a company "public" vs "private", you've about identified every business in the country in some form or another.
Outside of federal/state regulators, Brightline doesn't answer to taxpayers. They answer to shareholders.
I can't think of one thing that the government does better or more efficiently than the public sector - especially in transportation.
I’m always amazed at how capitalism in this country means industry gets to keep all the profits and socialize all the losses.