The more time that passes without a train leaving, the more people are waiting to take it when it shows up. The more people that try to get on a train, the longer it takes at a station. This is not a good combination: once a train starts being late passengers build up, so it gets even later and even more people are at upcoming stations.

The driver has little they can do but promise [1] a less crowded ride to people willing to wait:

The doors are closing. There is another train directly behind us. I repeat, the doors are closing.

How could the trains be set up to avoid this? One awkward idea would be add a second barrier, where the train keeps track of roughly how many people are onboard and only allows onto the platform a number of people proportional to the amount of available space. Where the capacity of the train is the number of people it can hold without getting slow. Another possibility would be to have trains announce that they're skipping some stops and run express when they get behind. Is there anything other cities have done that works?

[1] It's an interesting promise: as far as I know train drivers don't know where other trains are. But if a train gets slowed other trains usually get bunched up behind it. Passengers mostly don't trust the announcement, however, because (a) the driver doesn't know for sure there's a following train and (b) they know the drivers are mostly willing to say what it takes to get the doors closed and the train moving.