We have a person who has no other place to sleep. Right now we turn a blind eye to their sleeping in a park, and spend some time and money cleaning up afterwards[0]. Instead you would like to throw this person into a prison where we will spend even more time and money taking care of them from sunup to sunup? I don't see that as an effective solution to any of the problems at hand.
[0]:Which I agree, it would be better we didn't have to.
If they consume 100 square feet of land that would cost $1500 per square foot, the value is $150,000. (normal Manhattan prices, which should be less than the prime spots taken by these tents) It is unimproved, pushing the rent down, but small, pushing the rent up. Calling those even, a month of rent should be about $1,000.
That comes to something like $33 per day, or $12,000 per year. A possible solution presents itself: sell camping permits.
[0]:Which I agree, it would be better we didn't have to.