The sane way to privatize a transit system isn't to give the private company ownership over the system, it's to have the government own all of the plant and equipment and pay various private companies to supply or operate pieces of it. Then they're not deciding what fares are (the thing with no competition), they're deciding how much they bid to provide rolling stock or train conductors and then the government chooses the company with the most attractive bid for each thing it needs to buy in any given year.
The government in turn sets the fares by amortizing the total cost of the system over the number of riders modulo any taxpayer subsidies it intends to provide.
The half-nationalised half-privatised system you're suggesting isn't that far off the UK's approach, which results in almost zero maintenance, no on-platform support for disabled people and fares so high that people fly to other places in the UK via europe because it's cheaper than taking the train.
The government in turn sets the fares by amortizing the total cost of the system over the number of riders modulo any taxpayer subsidies it intends to provide.