There are always people doing disgusting things wherever they are but they are such a minority that it doesn't really affect the everyday experience of others in general. Maybe you only had a few bad experiences?
In many cities in the US, the answer is _nothing_.
I've ridden commuter buses in the US that had cloth seats and commuter trains that had soft plastic-like seats, and they were quite nice -- but they also cost twice or more as much as a regular bus/ train ride. That price cuts down on certain behaviors.
Probably nothing much to be honest. The train would get cleaned at the end of the line I guess. As to drugs, I don't think anything would happen either (apart from the other passengers leaving the car at the next stop) but people don't do that.
I think the problem is elsewhere, these behaviours just aren't supposed to exist in modern society. I don't know what is with the US society that enables them though.
For one thing, hard seats are not uncomfortable. A well-shaped wooden seat on a rocking chair, for example, is comfortable for hours. And most public-transport trips aren't long enough to really tax one's ass anyway.
For another: Public trains in the USA are a haven for homeless and bums. When you've driven past a coffee shop that has picnic tables on the sidewalk and seen a homeless guy with his pants literally filled with shit sitting at one... you understand the problem.
I don't care what country you're in; cloth seats on mass transit are dumb. They just can't be adequately cleaned. In Paris, a city allegedly suffering from a bedbug outbreak, I'd expect most people to question their use.