If it's not reclaimed in a certain period of time you might even get part of it for yourself.
You are arguing from your personal point of view and moral base. The law is more complex and continues to recognize that you do not have an absolute right of ownership to things you claim you just found around and about.
What “proper authorities” are those, if someone finds a $5 note on the street, as has been happening for decades? In 99% of the cases, the finder just keeps the money without making any attempt to find the owner(which will be near impossible to do anyways in a place like Time Square). How do you even determine that that particular $5 note belonged to some particular person? All $5 notes are virtually the same.
Back on point, exactly when did it become “stealing”, when you find a phone that someone has left behind, try repeatedly to return the phone to the alleged owner of the phone(as determined by data on the phone), only for the owner to refuse to accept it, and deny they ever lost any phone?