This format a) is more space efficient than JPEG at equivalent quality levels, and generally more efficient than PNG when lossless b) will be able to support >8 bits per channel, which would be useful once compositors support HDR and people want better but still lossy screenshots of media.
I slightly prefer this format over the other JPEG replacement candidates (WEBP and AVIF), since those have 10bpp and 12bpp limits; acceptable to be displayed again, but not as good if one wants to, say, do post processing on a (linear color space, 16f pixel) screenshot from a video game. AVIF also has seams at 8k tiles.
I have a prototype branch adding JXL support called
jxl under https://git.sr.ht/~mstoeckl/grim/ . However, I do not think it is will be worth merging in the near future, because: