It's economically viable here in Japan, and most public transit here is run by private businesses.
There's no way you're going to make public transit work in the American suburbs: you're better off hiring taxis and letting people use those for free, because at least the taxis won't create so much pollution and use so much fuel. Running buses every 10 minutes in the subways with 0-2 riders will never be practical.
How is it not viable in Japan? It's clearly working fine here. No, they're not subsidizing the trains with real estate; their financials clearly show that (though they get more profit from the real estate, granted), but there is a network effect: operating the train line brings foot traffic to the station and the area around it, making the land around the station very valuable.
Maybe western countries should learn a lesson from this, instead of somehow expecting public transit to always operate at a loss. The transit itself makes land valuable, so why not use that as an opportunity for profit? Here, even inside the stations, they rent out space to convenience stores, vending machines, cafes, etc., so they make direct profit just from that, but over in the US they seem to be allergic to doing that (nor do they even have bathrooms in the stations!).