That same argument should apply to public transport then. You can't on one hand argue that roads don't need to be profitable in the traditional sense because of their benefits and the turn around and ignore the same for public transport.

Even if you don't demand profitability, there still needs to be cost/benefit analysis done.

Do you build one rail line or two? Do you build one bus route or two? Do you expand a road or build a new one?

Making it a train vs car or rail vs road obscures the problem AND the solution.