Many train lines in Japan are funded in a public-private mix.
I don't want to overstate this too much, I dislike the JR privatisation (including a part where a lot of the public-era debt ended up in the gov't's hand), and all the train companies here do a combo of offering the train service and doing loads of real estate offerings at each station (making them very successful organizations overall). But I believe that we would see much less train coverage without continued gov't financing in these projects.
In both cases the people benefit, but in one the people benefit and it's still public property, whereas in the other the public goods were sold to business people and the business people are now getting a cut. [0]
If somebody is making money off of a transaction, that money is coming from somewhere. At the margins that is fine but when we're talking about 10s of billions of dollars it just looks like a handout from the general public to people who had enough money to invest in a transportation corporation during its privatisation.
Counterfactuals are not resolvable though, but I think we can look at how this stuff was built out and decide if there are structures to do it without having to just let go of democratic control of vital infrastructure.
[0]: yes I understand that there's a universe where the public-run version just falls apart and doesn't exist.
The US government spends about as large a percentage of GDP on healthcare as the UK does. It's just that in the US we double-dip for asking the users of healthcare to pay the same amount again.