I always thought that exactly this question was part of their demise. Although the word "synergy" is far overused, it's exactly what Yahoo never managed to create. Google brought people searching content together with people offering solutions. Facebook brought people seeking entertainment together with people offering entertainment.
Yahoo had it all - email, answers, news, stocks, search, and they even invented Hadoop back then to sift through all their data. They just never had any larger vision to integrate any of their assets properly to solve a grand problem.
They always just threw ever more noodles to the wall and tried to see which ones would stick.
There's zero coherency in anything they do, for me it's just a diverse bunch of poorly maintained and integrated services that's purely kept together with duct tape, page rank and marketing hacks stacked on top of each other.
It's the kind of slow death when there's just enough recurring revenue left that it's hard to screw things completely up, even with a league of completely dilbertized MBAs in charge battling each other until the last of talented people have left.