The world could have collaborated and built the modern Internet just fine on BSD licensed software, which is itself a variation of public domain. What Stallman deserves credit for is inventing the Copyleft license as a way to compel source code sharing. He's stayed relevant beyond that as source for paranoia about software being used against people, a stance that looks more prescient each year.
The BSD license very well could have worked, in the sense that I know of no law of physics or any other hard barrier making it impossible, yes. But generally to get something like what we've seen from the GPL Open Source movement, you need some kind of hedge against total selfishness. This is particularly true when dealing with corporations. That's the one thing the BSD license does not provide.
Perhaps in a more ideal world that does not still have such a pronounced scarcity mentality, the BSD license would have been sufficient. But in the world we know today, it's clear to me why one was more successful than the other (in terms of participation) long after a time when both were available.
I'll add, "paranoia" is one of those words that gets thrown around. Properly understood, it means an unreasonable fear of what is either impossible, or so astronomically unlikely as to be completely impractical. It doesn't take much study of history to see the repeating pattern that, again and again, any form of power or authority that can be abused, has been abused. Knowledge and technology are forms of power. It is inevitable that those who can wield them will abuse them. It's a scenario that is not only inevitable, but one that should be expected and prepared for.
To do otherwise is simply foolish and naive, an act of investing tremendous trust in institutions that have repeatedly proven themselves untrustworthy. I wonder sometimes if it's merely a problem of scale. If an individual lies, deceives, manipulates, or otherwise acts dishonestly towards another individual, confidence is quickly broken and trust withdrawn, often permanently. If a government or other large institution repeatedly acts dishonestly, you often see this faith-based (certainly not fact-based) defense that it meant well, will do better next time, and deserves our continued trust. This is usually never explicitly stated, but can be readily observed in the decisions many people make.