I dispute your assertion that those things are the broader long term interests of the whole society. Their unprofitability is factual undeniable evidence that they are in fact unwanted "services" who are having resources poured in to them not due to their own merits but due to political decisions unrelated to their merits.
I want to be very clear here, because there are many people who seem to be under the misconception that profitability is something bad.
It is not.
Profitability is literally a measure of how much value a given thing is providing to society. There is a 1 to 1 relationship between profitability and societal and individual benefit.
When you say "Public services don't need to be profitable" or express similar ideas, what you are actually saying is "Public services don't need to provide societal benefit".
For example, while I doubt many would dispute that having an active police force provides a significant societal benefit, actually capturing that value via a market-based system would be exceedingly difficult. (E.g. You just caught and jailed a murderer. Now, who do you bill for that?)
Thankfully, trains don't suffer from that problem; their value is extremely easy to capture (and thus quantify) via a ticketing system. But I felt I should point out that it isn't always so easy in the general case.
2. Good, it's a progressive tax, instead of being a regressive one. Transport costs disproportionately affect the lives of the working/labor class.
3. Market signals are only ONE factor to consider. And you don't need ticket sales to measure demand. Building infrastructure often creates demand where none existed before. Any long-term planning must also take into consideration unprofitable longer-term projects that provide immeasurable benefits.
4. Yes, the user has an incentive to avoid overcrowded trains. You don't need to fleece them for it.
5. There is no realistic alternative for large-scale infrastructure projects - these are natural monopolies. This is a rail network, not a software company. What is a user going to do if they don't like the service? Start a new rail company? An average citizen has more recourse with their local government than with privately-owned monopolies. They can vote at the ballot box every few years.