What's so great about webp? I haven't heard about it. Is it one of those jpeg competitors? Because I did see a blog post recently that said none of the the things people are coming up with are more than marginally better despite jpeg's age.
However, WebP works well for a much larger range of image types[0]. It has lossless options with better compression than PNG (because PNG is incredibly simple compared to more recent image formats, in my opinion in a kind of beautiful way). And when compressing graphically simple illustrations with lossy settings, it can get much better results than JPG, both compression and quality wise.
Having said that, I still hope FLIF (or some descendant of it) will get some traction eventually[1].