I get your argument about efficiency. But effeciency becomes less of an issue as hardware becomes more powerful.
The main reason I would prefer a native app is for the interface. If I am on my Surface RT without my keyboard and mouse, I would rather use a native app with a touch-first interface. But on my Windows 8 desktop, i will always use the browser. The website in almost all cases will provide the richest experience. So to summarize my thoughts - if efficiency is not an issue (in other words, the hardware can handle just about everything that modern websites need power-wise), the only time I would chose a native app when both the app and website are available is for the optimized touch interface.
Apps are absolutely essential on platforms without a full-featured web browser. They are definintely important on Windows RT, but just not as important IMO.