https://caniuse.com/webp
Any updated (modern) browser should be able to see webp just fine, I'd rather just serve it without a backup plan if I'm planning to have webp in my website.
The browser support for webp is fine, problem is everything else. If you only care about displaying the images (not letting people use them elsewhere), you only use lossless webp, and all your backend infra supports it, then sure.
Also, if users download your images and use them elsewhere, webp will still be more annoying for them. Though it's not very common that you want them doing that anyway.