The never-addressed problem is: the theory and most economic calculations ASSUME perfect knowledge of the marketplace on the part of both buyers and sellers.
Of course, the reality is such perfect knowledge never exists. In the case of the price of labor, the workers have poor information about what their labor is worth both in the overall market and even within their own company. Most firms have strict rules about employees discussing their pay, which is about the only way they could figure out if they’re being paid the same as others doing the same job. In the broader market, there’s precious little information about pay scales among different companies.
The same problem exists to greater or lesser extent throughout marketplace. Commodities markets can be manipulated because of this.
Unregulated capitalism leads to the kind of excesses seen in the late nineteenth century; with workers not being paid enough to support their families, and robber baron industrialists rich enough to buy the government. This was a real danger to the country, and the reason Teddy Roosevelt championed the estate tax (to prevent an American aristocracy based on inherited wealth.)
We have regulated the “free” market for over a century, and for the most part, it has been beneficial. Enacting a law that stipulates that maximum and minimum wages are to be set as percentages of each other within an individual company, would not be a “band-aid” as you said, but a solution that allows maximum freedom to the market to set prices for labor, while ensuring abusive wage dispararities are ended.