your concerns aren't unwarranted, but a lot of celebs walk around manhattan at all hours unprotected, and they take cabs too. i've lived in the city since 1990, and one thing i've learned is that New Yorkers are pretty jaded and tend to leave them alone and not even bother them for autographs. my own penultimate new york celeb cool experience was sitting next to Keith Richards in a nice restaurant late at night and just minding my own business. i stood in front of the late jfkjr and darryl hannah in, of all things, a car rental line and didn't say a word. the people who make a fuss over them are usually teeny boppers or out of towners. my guess is that someone like brady is less hassled in the city than he is in boston. if he went into a good restaurant in manhattan, he would most likely not be bothered.
why do the celebs do it? you'd have to ask them, but I think most do it either because they want to be seen or because they just want to act like the normal people they once were. manhattan, ironically, is one of the few places they can do the latter.
as for being "rich," it's the highly visible rich who seem to have more bodyguards on the streets of manhattan, but i have also seen robert rubin or george soros just walking down the street like any other new yorker on his way to the office with no tail cars or big guys with ear pieces and open jackets in the vicinity.
