Most mass transit systems we have were originally privately built and operated until they became unprofitable in the 1930s-40s at which point they were publicly taken over. More recently there has been a resurgence of "public-private partnerships" where a private company builds a project and then gets a long term deal to extract money from it once it's done. Denver's recent transit expansion is one example.

A potential downside is that we might end up back in the 1940s, when the subways became unprofitable and cities were forced to buy them out of bankruptcy because residents came to rely on them.