I’ve got plenty of lived experience.
Single mother then shitty relationship with more kids. Benefits, worklessness, poverty, awful sink estate in South London.
You know what she told/taught me? Not to be like her. She made some bad choices, she had some bad luck, and that combination entrenched her but it didn’t me because I wanted more and was young enough to be able to not be bogged down (no kids/debt etc).
I’ve never claimed benefits, not because I’m morally superior, but because I had a job from 16 including during study and I’m a professional homeowner owning a decent salary.
Some are like your description, many are like mine.
What I do know from my lived experience is that if there were no benefits for the third child we would’ve been starving as a family.
I don’t give a fuck if a few (because it is FEW in my experience) gaming the system benefit if the vast majority who receive it are in need.