I agree with your points, but I don’t even think you need to go that far.
No one has the right to tell me what price I can exchange my labor for or what price I can hire someone for. If I want to work an hour for $5, that’s up to me and my employer. If someone wants to work an hour for me for $5, that’s up to me and my employee. It’s as simple as that.
Also, Libertarians supporting the minimum wage? That’s not something I am aware of.