In Europe there's considered to be a 4hr limit to peoples' willingness to use the train. People will use a train from London to Paris but few go from London to French Alps or from London to Germany - it's just too far. In US terms New York to Boston is about the limit for a train I'd say.

Planes are vastly more efficient than trains - why spend billions subsidizing hundreds of miles of train tracks when you could just have a couple of small runways? Also UK train carriages cost over $1.5mil each (per carriage not per train!). In the UK trains are considered to be very expensive even through they are massively subsidized.

I'm struggling to think of a reason for their existence. Maybe it's because they're subsidized by the state so every small region exerts great political pressure to have their 'fair' share of the subsidies - once one town is connected every other town demands their fare share, otherwise they are at a competitive disadvantage.