For me it's very simple.
The welfare system is not some magic money tree from which we support everyone from without limits. Surely placing some limits on how much support one family can receive is entirely logical?
If a woman is going through such a bad time that "...their lives were just too hard. Too chaotic. Beset by too many problems for even the best-intentioned, hardest-working teams of social workers, health visitors, doctors and psychiatrists to solve." then I really find it hard to believe that the best answer is to just give them more money and say "Oh well..."
The welfare state is supposed to be there to help people in their temporary time of need. It is not there to fund a particular lifestyle choice.
For me, as I've said in another thread the sensible thing to do is draw a line as you enter the welfare system. And that's what you get benefits for. If you have more kids, no problem...you dont get more money though. For me this is fairer and less dangerous since you don't have the government in effect setting an approved number of kids.
That said if it's a choice between the status quo and a benefit limit of say 4 kids then I'd opt for the latter.