Almost all rail in Japan is subsidized, directly and indirectly. Yes the single line that is the Tokaido Shinkansen is immensely profitable; even then, JR Central does not pay market-rate interest on even the portion of the construction debt that was not absorbed by the government.

I don't want our public infrastructure to be profitable; I want it to be ubiquitous and frequent.

This is not true: Japan's rail systems are profitable on a cash-accounting basis (e.g. fares add up to more than day-to-day operating costs), but not if you include the immense cost of building the rail itself. When Japan privatized its rail, part of the privatization agreement included the government assuming most of the debts from construction, so the private entities wouldn't have them on their books. If you were to include these costs, Japan's private rails wouldn't even be close to profitable.