All of them. You don't necessarily need C, you simply need to not waste CPU cycles on things that neither improve the user experience nor decrease development costs. You could achieve this with a higher-level language, including something like ObjC and ARC.

Your position implies to me a myopic inexperience with web development.

I'm very familiar with the space. Every cycle counts -- if a cycle is not spent on user experience or decreasing development costs, it's a completely wasted cycle. Browsers waste mountains of cycles.

Modern desktop and mobile software makes heavy use of SMP (threads), SIMD, specific CPU-optimized code paths (in addition to SIMD, and requires that the basic platform infrastructure be as low cost as possible. You simply could not achieve glassy-smooth scrolling and other near-instantaneous UX otherwise.

I seriously doubt that you've ever built a desktop/mobile application given that you "can't think of an application I use on a daily basis that can't be done equally well in the browser.".