You cannot legally remove people from the subway for being insane. If someone is making me uncomfortable by regaling me with conspiracy theories and ethnic slurs, there isn't the clear legal authority to trespass them.
However, if one car costs $3 and the other costs $6, the person who is statistically likely to urinate on the seats is more likely to pick the $3.
I will honestly pay double fare just to sit in a car with others that can afford to pay double fare.
You absolutely can (and should) remove people for screaming racial slurs at passengers in public transportation. Most crazy people are able to ride public transport just fine without being abusive to others. No one should be trapped in a car with someone who can't meet that very low bar, crazy or not.
I've been to other countries where the public transportation was amazing, and unsurprisingly there were almost zero people urinating (once in Japan I saw a drunk salaryman passed out with his pants around his ankles at a station and he was quietly whisked away less than a minute after I spotted him) so it's not as if a nice train system for everyone is some pipe dream that can't work in reality.
However, if one car costs $3 and the other costs $6, the person who is statistically likely to urinate on the seats is more likely to pick the $3.
I will honestly pay double fare just to sit in a car with others that can afford to pay double fare.