It supports transparency like PNGs, and animations like GIFs, and is generally not a bad format on its own due to its balance of quality and file size.

The issue is that support for it is lacking; a large number of major media applications don't have any WebP functionality, meaning that an image being WebP format only adds an irritating extra step where you have to convert it to PNG to use it. The other issue is that the adoption of the format online is disproportionately high, compared to its adoption by major app developers. It's bizarrely common to download an image, only to find that you can't use it because your software (I.e. Photoshop, Clip Studio, OBS) doesn't support it, so now you have to either convert it to PNG somehow or hunt down a new file that isn't a WebP. For visual artists of all kinds, this is a tremendous pain in the ass, and it's pretty obvious that it doesn't need to be that way in the first place.