"doesn't want to" is an awkward way to look at it.

It's more of a catch-22. If you simplify 'welfare' to "If you're not above the poverty line, you're entitled to assistance", then a job which does not bring you above the poverty line is zero-sum - you're still entitled to assistance.

An example I see here quite often, is people who can only find part-time work, and still receive assistance. It's not unusual to find people in the position where they're working <20hrs/week, but do not want to work 20<n<30 hours a week because it'll interfere with their benefits.

This is not the "don't want to work" trope - they'd take 40/hrs week in a heartbeat. But if 20hrs/week + benefits is better than 25hrs/week sans benefits, who would realistically take more work for less pay?

Well, that reasoning was originally revealed to me by an economics professor, resolving the paradox "Germany supposedly has better welfare than the USA, why does Germany not have a minimum wage?"

So basically, that line is 100% standard economic thinking and therefore can be best understood and accepted by making the usual assumptions: humans as rational actors with perfect information and the cognitive ability to weight options, striving to maximize self interest.

https://en.wikipedia.org/wiki/Homo_economicus

If we're a a little more relaxed and maybe realistic with that assumption, we might find that it's a complex issue, with people's actions spanning a wide spectrum from "work? No thanks" to various levels of urgency, then desperation trying to find a new job and to make a living. Finally to people who'd be working hard even if unemployment benefits were 3x their wage, out of principle.

Point is, there are other factors to look at than the minimum wage alone.

Here in the UK, most people who get welfare are also in work, so presumably there is a large tax saving to be had in raising the minimum wage.