We've had this in the UK for years since the 70s; it's called child allowance and everyone is entitled to it. Child allowance isn't as generous (£21-£13 a week per child), you a range of other benefits such as tax credits.

The problem here in the UK is that the system is so generous that it has created generations of unemployable people that are dependant on benefits. If you are a women with one or more children you can claim unemployment benefits and get a property paid for by the government. The more children you have, the more benefits you are entitled to, so inevitably people in this situation usually have several children. In the surface this seems like a good scheme which helps poor families, but low social mobility means that children born into families that live off benefits are destin to do so themselves; so not really helping remove poverty but rather perpetuating it.

Admittedly I might be slightly biased, as I grew up in a poor family and knew many such families. There is a popular opinion that people choose to live off benefits in the UK, but I would dispute that and say that most people simply follow the path of least resistance; so the system is more to blame.