WebP images load faster than JPG and PNG images, so it is a good progressive enhancement, particularly if your site is image heavy.
But if by "only" WebP you mean there would not be a JPG or PNG alternative, I don't think that is a good idea because your images won't be available to people on Internet Explorer, which doesn't support WebP right now.
With updates like this its a good idea to look at how people are accessing your site. In analytics, are people typically using mobile or desktop, and what kind of browsers do they tend to use.
As far as whether WebP is possible in Wordpress, yes there are WP plugins set up for this.