A funny case in point: Sora.com produces WebP outputs, but you can't turn around and use them as inputs. (Maybe they've fixed that?)
Smaller websites almost always reject them. Even within big websites, support is fractured within the product surface area. You can't use them as Reddit profile icons, for instance.
One of the most apparent issues is that a lot of thumbnailing and CDN systems don't work natively with WebP, so you have to reject WebP outright until broader support is added.
Once the WebPs are in your systems, you have to make sure everything downstream can support them... it's infectious.
Really unfortunate that we haven't been able to move past this.
You can think about WordPress what you want, but afaik it does not allow to upload WebP files to its media gallery without any additional plugins while being said to run large parts of the internet...
Most websites break with WebP. Desktop tools choke on WebP.
It sucks, because it's a good format.