Either Gin96 is on a wind up or she's thinking of somebody specific.
Gin96 has a SIL perhaps or other acquaintance who, having broken up with the father of her first three children, who failed to support his children and isn't expected to in his social circle, has met a new man, who got her pregnant with their 4th child and also buggered off, leaving her reliant on insufficient benefits because nobody expects him to support the fruit of his loins either - no social pressure or heavy disapproval of deadbeat dads, so it doesn't happen - by the sound of it.
The benefits cap is reprehensible because it puts children into poverty, which any supposedly first world country should be deeply ashamed of. As others have pointed out it's also, on a totally cold, calculated level a misguided policy because children who grow up in poverty tend , on average, to be less likely to be able to contribute through taxes and socially responsible long term work as adults. Free childcare for 2 year olds in poverty is supposed to address this issue, yet the benefits cap takes away with the other hand - the children in the free childcare won't benefit nearly as much if they're living in a stressful environment because of constant intense money worries, the house is cold, there isn't enough hot water for baths and they're fed cheap junk food or going hungry because their parents can't afford anything better. Still worse if they're subject to the disruption and stress of losing their home due to non payment of rent. It's counterproductive.
That is a very specific problem, but the fact remains most people choosing to have 3 children have a long list of things to consider, with the benefits cap being irrelevant to people not reliant on benefits - relationship duration and security, savings, job security, coping skills, support network, health, needs of existing children are all far more relevant to most families.
I do have aquatintances who struggled very vocally with two children who openly announced the decision to ttc (announcing to a large group of friends and acquaintances the plan to ttc is a pretty strange thing to do in my opinion anyway, not announcing a pregnancy but a decision to have unprotected sex in order to conceive...) where I've inwardly thought wtf? When people are clearly really struggling (not in this case financially but emotionally) to cope with two children it seems absolutely incomprehensible to actively decide to create another baby. I really do wonder what's going on in the thought process there. Other people, of course, don't struggle at all and on an individual level have no reason not to have a bigger family - environmental responsibility is the only argument against for some people, and it's often hard to see that as a personal factor (more so if already pregnant than if thinking about whether to conceive).
Perhaps Gin96 should have posted a wider question about what people consider before ttc or going ahead with a third or subsequent pregnancy. Financial security should definitely be a factor, but making it about benefits makes this a question about a specific individual of GIN96 's acquaintance I suspect - or worse a general weird "anyone who did something I couldn't have managed should be shown to be wrong" slightly larger families bashing thread, or a benefits bashing thread.
I do remember, when I was teaching, a mother who kept on having more babies, every year more or less, and had four or five children in the school already with social services involvement but nothing severe enough to get the children removed. The older children were fed and housed (3 to a bedroom) but not supported. The father or fathers wasn't involved. The mother clearly had very complex problems and almost certainly learning difficulties and needed massive support, which even back then (pre austerity) she wasn't really getting. The home school liaison officer felt she really just kep having babies because she loved babies and couldn't really think long term. It's sad that there was no way for society to properly support her older children. This was pre benefits cap but it's unlikely that would have put her off at all.
Either way the scenario in which a benefits cap is a deciding factor clearly isn't generally applicable, it's a state applied punishment or gesture of political judgement on private lives which punishes small children. Punishment never actually works to change behaviour in the long run. The benefits cap was brought in to please a certain pool of right wing voters, not because of any real expectations it would influence family planning decisions.