Do any of the open browsers support it yet?
Sure there are JS polyfills but those aren't going to work well on mobile devices and until content creation tools like Photoshop and desktop operating systems like Windows and Mac support exporting and reading BPG, it's unlikely to see much adoption.
FLIF and BPG are development formats and where you look towards the future, not the past.
JPEG isn't going to morph into some brand new format that supports arithmetic coding. New formats will adopt those, specifically because they don't have to support decades and petabytes of files.
Not to mention, if you've ever actual written a JPEG decoder/encoder; the format is not conducive to coding outside of it's HUFFMAN/quantization format. PNG can add those things since it's actually an extensible format, but even then...why? It's not like the libpng everyone has installed will magically support them.
Arithmetic coding is just the one everyone knows since its taught in information theory 101 (e.g. Cover and Thomas).