You can still hear those things, just not obnoxiously loudly. NC works best against static sounds. Speech still makes it through. Just not as loud.

If you're in a busy car enough people will hear it to be aware, and if you're on your own you will hear the announcement clearly.

Besides it's really a one in 10 million chance you'll get stabbed on the metro, not worth worrying about. The chance of getting hit by a car in traffic is much higher. That feeling of always being in some kind of danger seems to be very American, I never really see that in people here in Europe. I think it's the sensationalism in the press there, every little incident is blown up to massive "BREAKING NEWS!" proportions.