That's a great turn of phrase. I'll try to use it the next time somebody asks me to summarize the GPL, which has similar restrictions built in as per Stallman's original intent.
To me it seems, banning non-competes, will create more competition.
Have you ever seen a large corp and how inefficient they are? The only reason they can remain large is because they can afford to buy politicians and legislation to keep their competitors small. Big Corp creates new regulations to protect their business, the most clear examples are in telecommunications and the music/movie/copyrightable industries.
If we removed more regulations today, the big corps would try and place them back to destroy their competition.
In a purely capitalist society wealth (power) accumulates at the top. Money creates money so whomever starts out with the most money tends to win. This is why highly capitalist societies turn into Dubai, with an ultra rich ruling class and a serf/slave class with little in between.
Just as an FYI (and apologies if you are already aware of this), but Standard Oil had already lost about ~25% of it's market share by the time it was broken up. Rockefeller had no influence in Texas and California where the wildcatters had moved to and found oil.
A regulation-free system is not a stable equilibrium, so the conclusion will not be regulation-free.
I'm reminded of the old adage "too much capitalism leads to too few capitalists".
That's not a strong argument either. You could substitute "contract" with anything. I say this as a staunch libertarian. Government restrictions aren't bad because "government", but because restrictions.
The free market works best when government restricts the freedom to restrict freedom. That's why cartels being illegal is good (they restrict competition), bans on insider trading are good (they restrict fair competition), etc. Non-compete restricts the freedom on the labor markets.
If you let people do anything they want because freedom, you don't actually get freedom.