I don't think mobile gaming will completely replace consoles, PC, or handhelds. Those are all specific platforms with their own benefits and drawnbacks. Mobile gaming is just a newer sub-market that has grown enough to influence the others as they have done to each other as well.
For handhelds, the controller is built in. With most smartphones, the only input built in is the touchscreen, which limits the games to either swipe and point and click controls or virtual d-pads and buttons *shudders*. If you want to use a blue controller, you either have to get one that doubles as a nice case for your phone, get one that attaches easily to the phone (which probably means removing your existing case every time you wish to play) or prop the phone up and hold the controller separately. The former two options also require that the controller fits your phone. Also, battery life and chip efficiency will improve as time goes on, yes, but so will the players' demand for better graphics and, in turn, the developer's demand for more powerful hardware. Furthermore, with a separate handheld, one can play games without worrying about the charge of their phone when they are on the move. The only thing mobile will do to the handheld market is possibly kill Nintendo's competition. (Regrettably, the Vita looks like it might become the first example.)
For home gaming, there might come a time when tablets/huge smartphones replace consoles. That either means the gap between console power and price to tablet (with HDMI output) power and price (with a controller) closes to the point the market chooses the later or cloud/streaming gaming becomes viable enough that a weaker device like a tablet, phone or even the TV itself will be all that's necessary. The cloud scenario is still years/decades away though, as the internet infrastructure of much of the world will still necessitate a full powered machine at home. I'd bet we will see at least one more console gen where the device can play all games fully themselves and the companies will simultaneously try to sell their cloud service to both the console owners and to users of third party devices.
There are still many people who hate the cloud only concept (Yours truly is one of them.) and/or will never have the internet connection to play games off of a server halfway across the region/country. PC gaming will probably be the haven those people flock to when no other market leader bothers with making a comparable ecosystem. PC as a gaming platform will probably also only die when we run out of the resources to make the components, as it is so open that no open company can truly control it. (Some can argue Microsoft, and to a lesser extent Valve, has the greatest influence, but there is always competition for both of them.)