The main argument against it is that many people loose their jobs when the minimum is raised for those who can't provide that much value to their employers. Any interference with the free market never results in a good thing. Note that the most innovative part of the economy, computers/software, is also the least regulated.
Because of interference with the free market we have safer air to breath, water to drink, food to eat, and medicines to take. The free market only cares about something when it will affect profit margins positevly and lets be honest most people don't care about how why it's really important to not pollute the ocean. Without government interference we would still have child labor. Correlation doesn't equal causation, my friend. Most would agree the reason software is so successful is because of the ultra low barrier to market entrance because all you need to build software is a $300 computer and cheap Internet connection. I don't have the burden of having to run a physical store and pay all the expenses that go along with that. I can compete with billion dollar companies and win.
Interesting theory - can you explain why, then, that the most regulated economies ever, such as the former Soviet Union or former East Germany, were the most polluted? Interference in the free market causes chaos, such as our current economy and the direction things are going now, unfortunately.
Your easy start up example is interesting too, as if there were more regulation, you would have to work through layers and layers of red tape and fees and lawyers to start a company etc which simply reinforces my point. If you were to add 50K+ to the costs of starting a software company due to regulation and fees, the innovation landscape would change dramatically as would the companies we have today.
There's no such thing as a free market. Just like there's no Santa Claus.
Also, some very innovative parts of the computer/software economy not only lack regulation, the FOSS sector, lack wages and salaries that are directly related to the production of said software.
It doesn't hurt that the software industry boomed under the Internet, which might be the most horribly regulated and managed infrastructure in history, but it is densely controlled by politics, else governments wouldn't have privatized their coax lines and wireless spectrum wouldn't be controlled by a few major players.
Also, software patents can easily be considered intense regulation, especially in the superfluous and artificial nature they make the mathematics behind algorithms scarce because you have to tip toe around getting sued.
