Have you actually been in any European country? Trains are heavily used for short, medium and long distance travel. High-speed rail in Western Europe is huge. Many many people commute via train or subway.

Profitability has absolutely nothing to do with it. High speed rail in France is hugely profitable, but the state subsides many lines because it's the right thing to do. Railways have a higher capacity, are much cleaner and faster, and are provided as a common service. You don't expect the fire department or forest service to be profitable, do you?