Marissa Meyer's tumblr purchase strategy isn't nuts, just the price ($1.1 billion?!?!)
Meyer wants to improve Yahoo's current products, and move Yahoo to a focused social media/portal platform. She's counting on Yahoo grabbing a piece of the mobile social media pie, which no big player has right now. (Google would be closest.) This is what will fuel Yahoo's "comeback" into relevance. The problem is that Yahoo has zero product presence in mobile. She's buying tumblr as an infrastructure purchase.
The next issue is pretty cool. Turns out, Facebook will probably not grow anymore. The tweens don't like Facebook. Kids don't like to treat their social media as maintenance work. And Facebook's zeal to grab eyeballs means parents have moved to Facebook, which makes it uncool. Kids want to maintain communication with their peers, so they're gravitating towards low maintenance social media, like twitter, tumblr, and instagram (which Facebook is borging to death). So Meyer buys tumblr to get more presence in social media, and deny another avenue Facebook can acquire to fix their mobile/tween growth. The problem is there's no way tumblr is worth $1.1 billion, unless Meyer is grabbing brains as well, and sees some sort of general social media on mobile framework she can build Yahoo on top of tumblr.