So if an employer and employee mutually agree on a wage that is below the minimum wage, the government will not allow it. That is dictating the wage.
No it isn’t. It is simply making your contract “illegal”. The same way that your contract with Bambie Delight for her to provide sexual services to you for money, illegal. Except in Nevada.
The same as requiring you to use a certain mininum gauge of electrical wire in your home is not “dictating” what kind of home you can build.
Did you not read any of this above???