I don't see how you in any way address what I said (in fact I mostly agree with you):
> I'd hardly call those "libertarian" societies.
I didn't claim that society has to be libertarian to not have minimum wage.
> If you have mobility of labor through your own free will, you are not a slave.
It's a different definition of the word "slave", and perhaps more precise, that you are using here. Technical word for what I mean, is, I believe, "precariat". It's not the same as slavery but there is often an overlap. And historically it's not obvious that one or the other is definitively worse condition.
For example, Czechoslovakia was communist. People were not free, yet they were economically quite well off. Today, people are politically free, but economically, some (although a small minority) are worse off. Because of that, I don't think it's obviously "disgracefully offensive" to compare the two situations. It's certainly not offensive to the poor people who make the comparison themselves.
> As was debated in prior threads, minimum wages are nonsensical from an economic (and welfare) standpoint.
It is only nonsensical if you subscribe to theories of "rational" decision-making, which do not hold for humans in practice. See for instance the ultimatum game, and how people respond to it.