I think you answered your own question: "I reckon that most users wouldn't even notice/realise if they were using another search engine".
For example, the other night I wanted to watch a movie. I entered the title in the Chrome address bar. Google was automatically used of course (yes it's customizable through a few menus, but for most people that means it's auto Google). The first result had an option to rent the movie. I clicked "Rent". Google Play was used of course. And I gave Google $3.
I don't personally mind this particular case, having long ago made the conscious choice to use Google Play over Apple or Amazon...or...ummm...for renting movies (mostly early Chromecast support). But it's a simple illustration of how Google isn't just a "search engine" that pulls up information you query when you want to surf the information superhighway. It's the automatic background interface for a great number of activities we do in our life. The fact most people probably don't even realize that is exactly one problem.
(And this has solutions of course, but it's one point to keep in mind.)