Without taking a side here, remember that education and police protection are also expensive. Few would agree to the phrase, “Education is expensive, so claiming so many children have a right to free education is idiotic on so many levels.”
Transit is very expensive and the cost / benefit needs to be decided by the public. Governments also need a plan to pay for it. But I would not say it is idiotic just because it is expensive.
The difference is that education and policing are not on-demand services, at least not in the way transit is.
I can ride the bus as many times as I like, and that creates costs for the system. There's no direct relationship between user whim and system costs for the other two services.
I see your point and agree that every bus ride is an additional cost. Keep in mind th at roads are also on-demand and generally not priced per-use. People generally pay the same for roads whether they drive a huge SUV every day that puts more stress on the road or have a small car they drive on weekends. Roads cost the same whether you use 1km to get home from work or need to travel 20km.
Roads are in fact overused and traffic is a nightmare in many cities because they are free. You could easily create a pay-per-use model for roads that charges based on usage. Instead roads are just seen as a public good used by everyone.
There's no reason why society could not treat public transportation the same way. I'm not necessarily saying it should be free. Countries with the best public transportation tend to charge something, but the goal isn't to cover the cost because transportation is seen as a public good.
Here we tax gas to cover the cost of the roadway. We are collecting more revenue from SUVs than a light compact. Electrics turn that somewhat on it's head, though.
Transit is very expensive and the cost / benefit needs to be decided by the public. Governments also need a plan to pay for it. But I would not say it is idiotic just because it is expensive.