Nice catch, David. I expanded on this comment in a post of my own and briefly addressed your concern here: https://medium.com/@pagerussell/you-dont-understand-minimum-wages-4b0eb0d308f6
The answer is, yes, you do reach a point where negative consequences come out. The number isn’t really important. What is actually happening here is you are decreasing the disparity of purchasing power between the lowest paid jobs and every other job above that. Those other jobs reset and adjust to the new min wage, but have lost a little purchasing power relative to the lowest paid positions. At some point, if you keep going, this means a janitor is paid as much as a doctor, and that [obviously] creates problems.
I haven’t modeled this, but I am pretty confident we are very far from such a concern. This actually sounds like a solid grad student dissertation topic. We rely on a century old model of minimum wage, and it needs updating. Its clear that at lower bounds increasing the minimum creates economic growth, like I roughly outlined, but it is surely a curve that eventually diminishes to zero or even turns negative.