The problem wasn't the trains themselves. The backup was at the ticket machines. They aren't enough for a lot of people trying to buy tickets at the same time, And if you have never used one, it's a bit confusing the first time.
When I was working in the DC area, I helped a number of tourists that were trying to figure out what to buy and where to go. If they were going my direction, I took them along in tow.
One guy asked: you aren't from around here, are you? :-)
I see, thanks.
My first thought was of the Shinjuku, Japan train / metro station with the “pushers” to squeeze the maximum number into each car. We had that experience and learned to avoid rush hours. Other than that, we only have experience with the uncrowded Bangkok systems. The joys of living in a small town.