The format actually has a lot of benefits - it supports transparency, animation, and compresses very efficiently. So it could theoretically replace GIF, JPG, and PNG in one fell swoop.
The downsides are that many apps don’t currently support it and that it’s owned by Google.
Personally I use webp for images that are not intended to share (e.g. banners and images on my blog), but stick to JPG/PNG for sending to other people.