Because the size is smaller and the quality is the same? Literally the same reason why you'd use any new image format, except that this benefit also applies to existing images, not just new ones?
I'm not against AVIF or anything, if you want to add future images which are using fancy animation features from AVIF then that's cool. You don't have to choose between image formats, you can (and already do!) use the right one for the task.
> tldr: I'm looking for a reason to care that I can losslessly re-transcode my old JPEGs. Ok, the re-transcoded images are smaller and exactly the same as before, but what is a real world reason why I would need that vs. using the old JPEG directly or re-transcoding it to AVIF?
You can use the old JPEG directly, but then your library takes up more space. If you re-transcode your old JPEGs to AVIF, you're losing quality or at the very least irreversibly changing the images.
I'm not arguing that it's the world's biggest deal or anything, but a free 20% size reduction on all photos in an image library and all JPEGs sent over the web doesn't seem like a bad deal.