Congestion is just what happens when too many people want to use a system and you're not willing to deny travel to some of them.

Congestion absolutely happens on trains. Just look at the New York or San Francisco subways during rush hour. The first and most obvious form is that you'll spend the first few train departures in "line" to get to the edge of the platform, then a couple more for a train you can physically squeeze onto.

The more insidious one is that public transit operators respond to crowding by increasing frequency beyond what their signaling technology can support. Even after you make it onto the train, you'll spend most of the journey stopped on the track waiting for the train in front of you to move.

You can solve congestion in any transportation system by enforcing a low enough number of simultaneous users, forcing the others to not travel, or use some other means. We seem least willing to do this with trains. Transit authorities are seriously thinking about congestion pricing for freeways, airlines raise prices at popular times, but rail systems are working to attract more ridership even as they collapse under the weight of their already-far-too-high ridership.