JPEG stands for Joint Photographic Experts Group. The whole point of the JPEG committee was to define a standard for lossy compression for photographs - so it makes a ton of sense that file formats based on this JPEG standard (like .jpg) are used in digital photography.
For the web however, JPG isn't the only image format that's used, so I don't understand how it's a 'clear winner' of anything. JPG, PNG, GIF, and SVG all see lots of usage, and while for some images they can be used interchangeably, they all have different strengths:
Why did the JPEG2000 file format never take off? I have one theory - there was a zero-day exploit found in many JPEG2000-reading programs that would allow a malicious person to embed a virus inside a JPEG2000 image, which would infect the computer of any person who simply viewed the JPEG2000 file. By 'opening' or displaying the file, the malicious code was run, which led many people to avoiding JPEG2000 for security reasons, and I've never really heard or seen it used since then. For a lot of people, this security vulnerability was the first (and maybe only) exposure to the JPEG2000 file format, so I don't really see people using it any more.