I don't understand why other factors would be mutually exclusive with "not wanting to work", or why you think good reasons to not want to work are automatically invalid.
FWIW, I have 3 children and have always worked. But I do know from years of being on mat leave/low income, that the system can be scary to navigate.
UC is also affected month to month by your earnings, unlike legacy benefits. That's fine for somebody like me on an annual salary paid calendar monthly, but lots of people, especially people more likely to be in receipt of UC, get paid weekly or 4 weekly. This fucks with their pay and can be a huge setback and source of worry.
Also, finding a job that fits reliably around childcare commitments can also be really hard. If you are a low earner in a part time job, which is what lots of mums in these situations are, then once you factor in the cost of childcare, and the costs of going out of the home to work, it can definitely leave you in a position where at that point in your life, work is not a practical or appealing option.
These days, it is true that on UC you are invariably better off in work than out of it, not least because of the work search requirements. But given the above, it's not that hard to see why "not liking" work, is hardly the driving factor in most parents' decisions, and as the OP knows full well that they're talking specifically about mums who earn little enough to claim benefits, it's very unlikely to be the main reason they are deciding to leave the work force.
From first hand experience, I have always operated on the understanding that while for some family set ups having a SAHP is a luxury, for some, it's a ball and chain, and is borne out of necessity.