Good point re: immigrants! I was making an inflation/wages argument, not a value-based one here. The prevailing minimum wage (for 95% of "low skill" jobs) is significantly different than federal minimum wages.
I think my point was actually a little off as well. Framing it as someone suffering for your cheap goods. Some things ARE like that. Fast fashion's $6 t-shirts come to mind. But service industry stuff like your cup of coffee - it's usually more like: does someone have to suffer so that you can get your cup of coffee and someone can become VERY rich off it.
And you forgot immigrants, the other large group working minimum wage jobs.