So the solution is private corruption where nameless corporations and CEOs get to take public money with 0 oversight instead?
I'm not a yank myself, but in the Netherlands the national railway (NS) is "jointly" owned but run as a private business and is a complete clusterfuck, exactly because we for some insane reason believe that running public transport should be profitable. Prices get raised every year (and we already have some of the most expensive train costs in the world), there's less trains, conductors get paid like shit and treated like garbage (hence them striking often), the trains are late more and more often, they're filthy etc. I don't want to drive, but if me and my partner decide we want to go to a different city by train, it costs us easily double what the equivalent car journey would cost. Of course, if we didn't subsidize cars as heavily as we do that'd probably be a different story, but that's venturing off-topic.
Similarly in the UK, privatization led to nothing but chaos there, and now they're left with ludicrous prices compared to all other modes of transport, because again, things are being run as a private business and they're expecting profits to be made.
Public transport should be a public good, and we should not expect it to be profitable. If it's possible, that's great, but we should aim for quality of service above anything else. How about we instead divert the gigantic chunk of money that goes to maintaining roads and making sure drivers have few inconveniences and instead start investing that in actual public transport instead?