I have to disagree, and hopefully can make a better job at convincing you than the other comments. In terms of search "google" is a verb for a reason, but I actually do think you could use other search engines, true, I agree.
What worries me is Android however. Perhaps not in the US, but in a lot of other places around the world Android is the only operating system accessible to people and a large majority of the market, since iPhones are an impossible purchase. Phone manufacturers depend on Android like computer manufacturers once depended on Windows.
Apple is raking in the profits because it controls the vertical and sells expensive phones in premium markets, but in terms of raw market share things seem to be shaping towards a Mircosoft/Windows like situation. Android is close to passing the 75% mark [1] and judging by sales it probably will [2].
Maybe we're still not quite there, but it's shaping up in that direction. Facebook def has the lion's share on social networking, and messaging, but I can't help but believe that when it comes to Facebook it's mostly network effects keeping people in, since there are plenty of other (and sometimes better) messaging apps, lots of photo-sharing apps, and alternatives for event planning, getting your news, posting updates, etc.
Idk if "Google should be hauled in first", but it should def be hauled in too (alongside Amazon, but that's a whole other story).
Tbh, Google has a monopoly over search, but Facebook does not have a monopoly over social networks. Bing and DDG are much smaller competitions to Google in comparison to what Twitter, Snapchat, et al. are to Facebook.
This means you don't have much choice when it comes to search, but you do when it comes to social networks. Obviously, you can live without both; but if you need both search and social networks in your life, it's obvious which company is more powerful. (IMO you can live without social networks, but not without search engines.)
