While support for more efficient image formats might be nice, there's arguably much less of a need there. Today's internet connections are mostly fast enough, and server costs are cheap enough, where the bandwidth required for downloading images is generally not much of a concern. The same goes for storage, where hundreds of high-resolution images can be stored for a few cents. With video, the file sizes tend to be far higher, so there can be much more benefit from moving to a new format.
And most importantly, the standard JPEG format is pretty much universally supported in software and on computing devices stretching back a couple decades. And for lossless web images, PNG is widely supported, at least for software and devices from the last decade or so. Software doesn't tend to change overnight to support the newest image formats, and if a format isn't already widely in use, there's even less incentive for developers to devote resources to supporting it. The PNG format came out in the mid-90s, as a much improved and open alternative to GIF, but didn't really receive full, proper support in all major web browsers until close to 15 years later, despite there not really being any alternative for lossless web images.
JPEG XT offers some additional features like HDR support, but HDR-capable hardware is still not all that widespread, and HDR images are relatively rare. So there arguably isn't that much need for those new features at the moment. And of course, there have been lots of other file formats pitched as being "JPEG successors" over the years that haven't really taken off. JPEG 2000, JPEG XR, WebP, HEIF and so on. And even if a format gets implemented properly in all major web browsers, most will likely stick to the older formats for some time, as there are lots of older devices that won't be compatible.