webp is fine for web publishing.

I have a problem with websites that use middleware that makes webp masquerade as jpg or png. so when you go to save it locally, it's a surprise webp.

not only that, webp is a standard that google made and pushed into the web consortium. I explicitly hate anything Google forces on the Internet.

The lossless mode is great (but more limited than PNG), the lossy mode sucks though. Like it only supports a quarter of the colour resolution compared to formats like JPEG.

Also being a video format, it's not actually tuned to store still images, it likes to blur/smear things.

Edit: But if you're using it for the intended purpose, low resolution previews, thumbnails and stuff like branding, it's fine. I wouldn't use it where quality matters.