I'm guessing that the strategic advantage is to cut off Apple's knees. Apple's key differentiator has been design; this filters down into all the apps written for their platform, so that consumers say they choose iOS "because the apps are better-designed". Google wants a critical mass of iOS & web developers to choose Material instead, and make the Material design good enough that users won't prefer native iOS apps over Material apps. Then iOS becomes a fragmented mess of native, Material, and Cordova/PhoneGap apps, while Android is all unified Material design down to the OS, and mobile websites just look like Android.
IMHO it's brilliant strategically, though it's kinda dick-ish toward Apple. There are a couple huge unknowns though, like whether startup founders will adapt Material, whether those that do become large mobile successes, and whether Apple will even allow Material apps into the app store (they've been known to ban PhoneGap apps before for not following native look & feel guidelines).