If you're are at a point where you're on benefits then you're also probably at a point in your life where having more kids is a bad choice.
The benefit system is a safety net, it does not exist to encourage people to have more kids to double their payouts..
I worked for years at an advice agency, and met thousands of people who had claimed benefits. The scenario you're describing isn't common at all.
That's a tabloid's version of the benefit system - when the reality is that most people don't want to claim. Most people don't want to have lost a job, separate from a partner, have to look after a sick relative, or one of the myriad of other reasons why most people actually claim benefits. The world is full of people who mostly want to get on, and have a good life that doesn't involve that kind of hardship. Most people didn't plan to claim benefits, but when circumstances change, they have to, and we shouldn't be punishing kids for that.