If you don't then you're simply a hypocrite (and worse).
Nope. I have no personal relationship with the child that's worth preserving. And in any event, my tax money goes to help support children all over the country. So does yours.
My not supporting a random kid doesn't make my a hypocrite. This is the kind of stunted thinking that I see often on FR lately. What would make me a hypocrite would be if I were in the type of situation I describe and deny my role as the father figure to any children I may have had that weren't mine. That would make me a hypocrite.
Not indulging in your deficient hypothetical doesn't make me a hypocrite. Look up what the word means.