Government provided services are not necessarily meant to be profitable in the business sense. It is enough if their global benefits are worth the cost, even if those benefits cannot be captured as direct profits.
For example public transit is worth a lot more in external benefits than just the fares paid.
It’s not about making a profit versus not—these prizes would almost certainly not be profitable for example. But you have to set high enough prizes to create the right level of incentive. Likewise, your (prices + subsidy) for transit or water/sewage must be high enough support an efficient level of infrastructure spending. With transit, the government underpriced and undersubsidizes. With water/sewage, the government under prices and doesn’t subsidize at all.
The government underprices for the same reason it underfunds pensions and over promises pension benefits. It’s a way of pushing costs into future generations while buying votes in the short term.
For example public transit is worth a lot more in external benefits than just the fares paid.