Google is darn near close to a monopoly on search (at least, Peter Thiel made that the premise of Zero to One), which isn't to say they're also a monopolist in every other field they're in.
I like Google since they're one of the few companies that has a 20+ year record of being careful with user data, but how much they control (or at least facilitate) is pretty scary from an objective viewpoint.
An information good is one for which it's very cheap to produce additional units. Unfortunately, I'm probably abusing the term, since books are listed as an example of information goods. The idea is that most of the cost of producing the book goes into the content (writing, editing, etc.) and actually printing one additional book is cheap. (When I said books are "imperfect" information goods I meant that they still require paper and shipping and retailing and such, but it's probably just a bad use of the term.)
There's a fantastic book about the economics of information goods called "Information Rules" ( https://www.amazon.com/dp/087584863X ). Software is an information good so this covers some topics relevant to the digital economy. My favorite part is the chapter on lock-in. In particular the discussion around the equation:
profits from a customer = quality advantage + switching costs
which puts "(marginal) goodness of your product" on equal footing with "pain you can inflict on your customer for leaving".
If Google is the monopoly in the sense that the OP describes, then a unified Internet itself is a bigger monopoly. Break apart the monolith of the Internet itself, and you have more player contending equally in facilitating search etc.
Google's core technology is search facility. If someone does this better than them, then there will be no monopoly. The core feature of printing press stood as is for longest period of time (even Xerox did not bring anything "new" to the table). That's, until the Internet in fact, was able to put a dent on the core invention of printing press. People are now reading on their screens, where as previously, they used to read only on the paper.
You are stuck with the short-term view of monopolies and privacy issues. We wouldn't be surprised if there was a big brouhaha over privacy during the time of the invention of printing press (ask any religious scholar what they have to say about the history of churches against the advancement of technology and knowledge).
The problem is, this isn't necessarily true. Microsoft used to make the same argument in the '90s. The point is when you get entrenched in so many areas it becomes hard to switch. It's a network effect of information rather than people. There would have to be a significant improvement in order for people to switch (with some other motivation, like political).
In bothe these areas, and others, they benefit by network effects, which I'm coming to see as foundational to natural monopoly and rent-seeking.
I simply don't understand what you're trying to say by mentioning the printing press in this context, though you might want to look up its particular disruptive history. Elizabeth Eisenstein is recommended reading.
Now, your kids are the next product.
Mr. Rochelle, the Google executive, said that it was important for the company to have large, diverse sets of educational users giving feedback — otherwise it might develop products that worked for only a few of them.
Why would they fail to provide that breakdown?
Because then they would have to admit they're building a profile of that child from the minute they start early school, and how strange that would be.