The problem is, how can you get the money out of men who fuck off and start new families without punishing/penalising/disadvantaging them ?
I believe that in New Zealand, they have a law that the number of subsequent/other children is not taken into account when deciding the level of child support owed. I think that's fair I'm afraid. You don't get to go and create yet more children that you can't or won't support (or create them with a non-supporter) and then use those children as an excuse to make the existing children suffer.
I'm basing this on my ex-neighbours, I used to be a bit friendly with them, before they started very vocally complaining and campaigning aginst this law because he couldn't afford to support his eldest child back in NZ because they've chosen to have two more children.