Punish them how? Here in America (and especially New York) we have a "two-party" system that works arm in arm to steal as much money as possible to line their own pockets. Voting for a different party doesn't mean getting a different policy - it simply means that patronage money is going into the pocket of different politically connected cronies.
I think the difference in the US is much more fundamental, pluralism is baked in to the culture in a way that is pretty unique anywhere in the world, so people have very strong reactions to members of other tribes seeking authority over them. This has gotten very explicit recently, but the dynamic was always there.
All of these things remain exactly the same no matter how much people cry about Trump, or wear pussy hats, or scream about 54 different genders or how "white supremacy" is the problem. All of these substantive policies would have been identical (and run by many of the same people) had Hillary won the election. In reality, the .00001% of the people who own this country and both corporate parties are laughing at all those people while they continue to rape the people and steal our freedoms.
If the MTA were simply a city agency for which the mayor was directly responsible, it would be possible to channel voter anger (and there's plenty of voter anger, by the way) into action. But it's the governor who really has the most control, and he's responsible to a wide swath of voters outside the New York City region (who tend to want less spent on the MTA in any case). Plus many voters don't really understand how the MTA is structured, and elected officials can hide behind this independent-agency arrangement.
If the subway service in, say, London or Tokyo or Paris became as bad as some of the systems in the US, it would be a major political scandal and the people running the city would fear for their jobs. That doesn't happen in the US, even in places like New York where a majority of commuters use public transit regularly.