A friend of mine who lived there for a while commented that that's because the police round them up and ship them out to the suburbs where they're not being seen by the tourists. They then migrate back to the centre over time because that's where they can beg, and the cycle repeats. Nothing is solved, no-one wins, and people die because of this policy, but at least the tourists are impressed by the lack of street people.
Moving drug addicts off the subway does literally nothing to solve the problem, except it keeps the subways nice and clean and allows everyone to think the problem doesn't exist any more.