However, you miss the important part of the equation, and that is skilled positions are going to demand more in compensation as a result of unskilled positions creeping more towards their earning levels. We have seen this for decades now, so we have actual empirical data that bears this to be true.
You may find this unfair, but by design these are are incentives to work harder and learned skills that will be desired by employers.
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?