If u are looking for evidence that the min wage is intended to set wages lower than market conditions here it is. Walmart wants the gov to raise the min wage so that a "price" can be set for labor instead of allowing the market &supply/demand to do it.

cnbc.com/2019/06/05/wal…

This is overlooked by most. The federal min wage does not raise wages it sets wages so companies can point to it and say this is what everyone else is paying. Sure, it increases wages for a few but in the grand scheme of things it lowers/locks in wages for many, many more

Now that the labor market is tight, companies are competing for labor and as the supply shrinks the price of wages goes up. Companies don't like that. They want a set price to stop workers from asking for more.

There is always at least two sides to an issue. The companies and gov only want you, the worker, to see one side of the min wage. They don't want you to see how it limits wages. This is why you don't see many companies asking for an increase (at least until full employment).