So far you've included university research (Google), large public companies (Xerox), state-sanctioned monopolies (Bell), companies taking advantage of network effects (Facebook), startups (Google's big innovation was in search before the company was born), and anything funded by governments in your definition of a monopoly.
If you define monopoly in such a broad way it's really not surprising that most innovation happens there, because your definition encompasses most of human endeavour.
You're misstating the categories. I'm making the distinction between organizations that are insulated from copying and competition and those that aren't. Xerox at the time of PARC wasn't just a large public company. It had 100% of the copier market and was insulated from competition by its patents. It was a large public company monopoly.
Google and Facebook, circa 2014, also aren't your typical public companies. Google is protected from copying because they don't ship a product. Their algorithms are hidden behind a web-API, and they are kept essentially as trade secrets. Facebook enjoys network effects, which provide protection from competition and in antitrust economics are considered a factor that gives rise to natural monopolies. E.g. the Microsoft and Offices monopolies were built on network effects.
It's obvious why government-sanctioned monopolies, and government and university research labs are insulated from competition. It doesn't matter if people copy their work, because they don't need to make profits in the market in order to secure their funding.
I'm purposefully excluding start-ups and public and private companies that don't enjoy substantial protection from copying and competition. These make up the bulk of economic actors.
If you define monopoly in such a broad way it's really not surprising that most innovation happens there, because your definition encompasses most of human endeavour.