WebP does not offer any compelling reason except a promise of space/bandwidth savings over JPEG. It doesn't currently support multiple color spaces, color correction, an alpha channel, or animation. It's promise of space savings at various quality levels is ridiculous because like they did with VP8/WebM Google is only focusing on PSNR measurements. PSNR makes for nice graphs but is not an effective measurement of how images actually look to people. An image that scores well in a PSNR test might look like shit when you actually compare it to the source image. Most JPEG encoders are tuned for psychovisual performance, not to score well in PSNR tests. Testing WebP vs JPEG with VQM tests would be far more appropriate but I suspect WebM would do far worse than with PSNR (since that's what VP8 is tuned for).
Without a VQM test it's really not appropriate to say that at a given size WebP has better visual quality than JPEG. Even if this turned out to be the case it's missing a lot of other important features that JPEG either has or a truly viable replacement for JPEG should have. WebP only supports a single color space and color profile so if your source images look like shit in that space or with that profile you're out of luck. JPEG can declare an image's color profile or provide its own ICC. It doesn't support lossless encoding or an alpha channel (right now) so it won't be appropriate to replace PNGs and GIFs which are often less optimized for the web than JPEG. It also doesn't support animation which for good or ill is still an important use of GIF files.
Yet another image format to not get widely accepted on the web doesn't do anyone any good. Why not help support JPEG-2000 or JPEG-XR? Help PNG out with a F/OSS compatible LZMA library. No camera manufacturers will support it because they can't just write a few Exif tags and attach an ICC profile and have a usable image. Converting your personal library means you get not only a lossy-to-lossy conversion but lose the ability to do lossless editing (rotation etc). Because WebP has more complicated encoding than JPEG it's going to require more CPU power to decode, your iPhone an Droid will get worse battery life browsing WebP content than JPEG content. The reduced file size (assuming WebP lives up to its promises) isn't going to make up for the vastly more complicated decoding. So hooray, Google managed to reuse their VP8 encoder for still images while simultaneously not solving any actual problems with images on the web.