Transit is actually never free, you either pay for it from fares, or from taxes, or a combination thereof.
Since mass transit access is something you can't badly overconsume in a sensible way, nor can you hoard and resell it in meaningful quantities, it does not noticeably suffer from the problems that plague free-to-take physical stuff. If keeping the access infrastructure is expensive, shutting it down and making access free may indeed save money. See how it works e.g. for public parks and city streets; both are toll-free.
Since mass transit access is something you can't badly overconsume in a sensible way, nor can you hoard and resell it in meaningful quantities, it does not noticeably suffer from the problems that plague free-to-take physical stuff. If keeping the access infrastructure is expensive, shutting it down and making access free may indeed save money. See how it works e.g. for public parks and city streets; both are toll-free.