The difference is nobody sees firefighters saving a homeless man and thinks "Eww gross I'd rather not have them saving lives next to me."
When public transportation gets the reputation of being the place of juvenile delinquents and petty criminals, people start to ask why their tax money is spent on it, and it becomes a self-reinforcing cycle.
I may sound like a cold bastard but I'd rather have public transportation system frequented by middle class families and commuters, because that's how you get these people to demand more public transportation.
The fare has to be low enough that poor people can afford it because they have to be able to use mass transit to get to work. Even the homeless need to be able to use it so they can e.g. get to a job interview. And a fare is not going to be a deterrent to juvenile delinquents because they're the ones jumping the turnstiles.
But if you're not actually excluding the deplorables then the fare is just a regressive tax and a deterrent to mass transit use for everyone.
The real problem is that you have unsheltered people without taking effective action against it and then the subway is a form of shelter. If you want to help them then you fix the zoning so more housing can be built, provide shelters, etc. If you want to be a cold bastard then you give them a one way ticket to a lower density city. Charging 10% of the cost of the transit system as a fare, which costs about as much to collect as it generates if not more, is neither of those things and counterproductive.
When public transportation gets the reputation of being the place of juvenile delinquents and petty criminals, people start to ask why their tax money is spent on it, and it becomes a self-reinforcing cycle.
I may sound like a cold bastard but I'd rather have public transportation system frequented by middle class families and commuters, because that's how you get these people to demand more public transportation.