Plenty of people take taxis between Manhattan and Brooklyn. A significant percentage of rides home to Brooklyn from Manhattan bars at night are in cabs, for example. The fact that you think everyone in Brooklyn is "poor" or that only rich people take cabs shows how inaccurate your knowledge of NYC is.

I've tried to address your other concerns in other comments. Just because you don't get dropped off at your place doesn't mean no-one else in NYC does ever.