You are right that the unskilled jobs are never going to pay more unless, 1. The gov’t increases the minimum wage; or 2. There is a severe shortage in unskilled labor; or 3. The Mexicans and Central Americans get homesick’ or 4.Aliens land and make a change to the DNA in humans.
That being said, yes, a higher minimum wage would result in all workers getting a bump. The guy who makes $10/hour would get one. Is this a bad thing? The middle classes have been declining for years, and cheap labor, out sourcing to China, and “Free” Trade are a big part of the problem. Maybe what you see as a bad thing is a good thing?
As for severe shortages of of unskilled labor, unfortunately it will never happen. What you may accomplish with reducing incentives is creating even more unskilled adults. Even if the minimum wage was raised to 50.00 per hour, they will never gain ground. Because the ground will alter making their gains non-existent.
The only ones who can change their station in life are those who wish to change it. False propping up does not work.
You cannot change someone's IQ by raising the lowest IQ number, nor can you create a living wage by raising the minimum wage. Propped up minimums only shift the scale, but not the realities.
Can't you see the flaw in your logic? It sounds good on paper, as well as, the spoken word. Reality is reality and reality takes over, while good intentions fail. You create an endless cycle that ends with increased misery, not less.