Trains *can* get stuck in traffic.
On my recent business trip to San Francisco, I got to see how a city with an actual functioning light rail system works. I was advised before the trip to not rent a car, and I'm quite glad I took the advice. I never needed the car, and from observation, parking in downtown SF is a nightmare. The only distance traveling I needed to do while in the city was between the airport and downtown, and for that I took the BART. On my trip into downtown, I soared high above the rush hour freeway traffic, and even affording nine stops at intermediate stations, I still reached downtown within about 25 minutes.
My trip back to the airport at the end of the trip was more interesting. About 24 minutes into the trip from downtown, the train slowed down and stopped on top of the high curved ramp leading into the airport. We waited for maybe fifteen minutes on the ramp about 70 feet above the Bayshore freeway, with the train banked at a 20 degree angle. At one point, the train operator came over the PA to explain that we couldn't pull into the station because the platforms were full of trains, and there was no room for us. We just had to wait on the flyover ramp until the platform cleared.
I submit to you, Ben, that trains do indeed get stuck in traffic.
I found out later from asking a security guard that the airport had gone into some sort of lockdown mode, and the trains hadn't been allowed to leave until the TSA was good and sure everyone had been inconvenienced. This was confirmed by the 55 minutes it took me to clear security. Fortunately, I had given myself plenty of time, and reached the end of my trip without further incident.

