They kinda already do. Google is built in, just search right in there url bar. You also got DDG, Bing, Wikipedia, Amazon, EBay? They make it easy to add YouTube, I wouldn't be surprised if you could add Facebook.
And like every browser does that. It's been that way for like over a decade...
Okay, and? Is anyone complaining about being able to search your favorite search engine from within Firefox?
Do you genuinely think this is comparable to Facebook integration? Do you believe that it Mozilla announced Facebook account integration and a Facebook side bar tomorrow, people's reaction to that would be, "oh this is just like what they did with search, this is fine"?
If not, isn't your comment a tiny bit disingenuous?