Google, Twitter, Yahoo and Facebook all hold patents which will make you go "wat. that is patentable?". They aren't nice guys. And all of them (except for yahoo) are holding de-facto monopolies.
Every large tech company wants a patent portfolio, as a defensive moat.
But the companies I mentioned don't actively engage in shakedowns, as far as I know; I left Microsoft off of that list because of its poorly disguised attempts to destroy Linux through patent trolling, and Apple because of the Samsung case, and Oracle because of the Java case, and Amazon because of one-click ...
In contrast, I don't see something like this necessarily being against the best interests or modus operandi of the companies I mentioned.
I can see it being unpractical, unlikely or unattainable for a variety of reasons, but those companies have de-facto monopolies, not state-granted monopolies (patents), and that they seem to prefer to operate in a world where you're allowed to innovate.