I have very mixed feelings about this issue.
On the one hand, I think state benefits for families can, if not well thought out, have long term negative effects on how people make decisions and ultimately social norms. There is a reason the advent of certain kinds of benefits corresponds to a sharp increase in unmarried parents, for example. Of course in some cases it is better for people not to get married to bad partners, but it's also better if people don't make choices that could lead to pregnancy with a dad that is going to be a bad father. Doing so can become normalized in a culture though, it's completely normal in my partner's culture for example. And it's not great for the kids.
On the other hand we clearly don't want kids living in poverty.
As far as capping at a certain number of children, I don't think that is the answer. We help these kids not just to help the parents, but because even though they are children they are citizens who need the help of society. You can't grade citizens based on their birth order.
I tend to think that the way forward is to think hard about how we want to shape society so people can afford to have kids - housing is probably key here. And also to encourage people to recognize the importance of trying to have their families with a committed partner. of course sometimes that can go wrong, death, divorce, etc. But the number one thing that predicts good outcomes for kids is parents who are together, so if we can discourage poor choices in this regard that would go some way toward reducing the need for benefits.
Mainly though it seems that this is a social value, and not one society is likely to try and make fashionable again.