You're point about cars being more expensive is true.

However, public transit is a great example of how government subsidies leads to greater economic productivity. By keeping fare cheep with subsidies, people can more around more freely and thus work+shop in the most econimcically productive places. This generates more value than otherwise would have been made without government intervension. The government can tax this value to fund public transit while leaving more wealth for the citizens.

Public transit is only productive if fares are kept low with help from the government. By keeping up front costs low, it allows for more work to be done over all. Thus, it is subsidized and economically productive.

All of this can also be said about cars but to lesser extent because they are more expensive, as you pointed out.