I think with images, just as with videos, there will never be a consensus; some people will insist on certain proprietary formats, forever. At least there's standards now, so that you can provide fallbacks - if you as a website owner would e.g. prefer people use webp because it compresses more than jpg then you can offer both, without forcing one or the other on them.

I wouldn't mind a solution on the server-side though, where in your html you just put an img tag and the server determines what the best format is based on browser support. Of course, that would mean there'd be a header (or some smart user agent analysis) for every image request, and you'd like to keep that overhead to a minimum.