Very simplistic view. A worker at $15/hour isn’t as productive as someone who also makes $15/hour - that happens every day at all levels of the labor industry.
There is a net economic loss - externalities imposed on society - to people working at jobs where their basic needs aren’t being met. That comes in the cost of mental and physical health issues of the worker as well as their family through their inability to properly care for their children; which is a humanitarian issue but an economic one as well because those children don’t reach their full potential. Police, jails and health services all have this burden fall on them, and we all experience a lower quality of life as a result.
What point is there pretending that the giant debate about minimum wage doesn't exist? These points have been argued to death. It is not like everybody hasn't thought of "with a minimum wage people whose labor is worth <15$/hr won't be employed", and that's a first-order "naive" observation that is only useful when considered alongside all the other arguments that correct it.
If a person working can't afford basic expenses they're slightly better off than not working, locally, but at a policy level neither outcome is acceptable---and part of the solution is to ensure that there is a floor because, surprise, employers will pay powerless people less if they are allowed to do so. It is a tradeoff between "making some jobs uneconomical" versus "putting a floor on people's ability to be exploited", and the obvious next step of logic is to look for, given that that floor is in place, what other parts of the economy will transform around it? Well: some jobs are removed (bad maybe) but other jobs will pay more than they would (good maybe), plus some prices for things will go up (bad) but they go up in a way that allows people to make non-exploitative wages (good), which means that the much richer and greater-agency employers may have to share more profits with labor (good) which means that some business ventures might not be profitable anymore (maybe bad) but then they'll have to innovate to find more profitable ones (good)...
etc.
Pretending like there is one argument and ignoring the rest of the picture is ignorant and a waste of everyone's time.
There is a net economic loss - externalities imposed on society - to people working at jobs where their basic needs aren’t being met. That comes in the cost of mental and physical health issues of the worker as well as their family through their inability to properly care for their children; which is a humanitarian issue but an economic one as well because those children don’t reach their full potential. Police, jails and health services all have this burden fall on them, and we all experience a lower quality of life as a result.