If there is a job that does not pay for a living, then there are two possible reasons. Customers actually value the work enough and pay enough for the product but the business owners take the money. In this case there should be a minimum wage cutting into the profits of the business owners making it a viable job.
On the other hand customers may not value the work enough and the job is just not viable, there is no market. Then you have to either bring the costs down by improving efficiency or automating it, or the job has to go away. Not paying a livable wage to the employers is just exploitation, giving benefits to the employers just means subsidizing the business owners and customers.
I am a bit unsure about the scenario when we just let the job go away and have a new unemployed we may have to support with benefits. Wouldn't it have been better to just subsidize the job a bit instead of having to pay for a new unemployed? But that of course creates incentives to underpay employees and take advantage of subsidies. It is probably harder to reason about this case because it is now a dynamic scenario and it is not obvious how things will turn out.
I am still struggling a bit to follow your thought process but I think you may have a point. I will probably have to add something later.
If we are in a situation where a part of the population is plainly unable to perform any work that pays for a living and we are unable to improve their skills, then we are really is some kind of trouble. They would essentially be like handicapped people. In analogy we would have a moral obligation to support them and it seems better to let them do some work not paying for a living and provide benefits on top of that instead of just having them fully on benefits. Kind of contradicting what I wrote above. And we are also back at the point from above of creating incentives to underpay employees.
The obvious solution would be to not get into this situation in the first place, to heavily invest into education and training. But if that is not good enough? How does reality compare to this scenario? What is the outlook? It is also not obvious to me whether a universal basic income or minimum wages and a conventional welfare system would provide better incentives. But I think I now at least understand the argument.