Since the recompression is lossless, you don’t need every tool you use to support it, as long as one of them is one that can do the decompression back to JPEG. This sounds a bit like complaining that you can’t upload .7z everywhere.
AFAIK downconverting to jpeg is only an option for legacy jpegs that have been upconverted to jpegxl though. Many jpegxl images likely won't support downconverting if they were created as jxl from the get-go.
Basically, jpeg->jxl->jpeg is perfectly lossless conversion, but a newly-made jxl->jpeg is not, even if it doesn't use modern jxl-only features like alpha channels.
With that in mind I'd actually prefer if those were treated as separate file-formats with distinct file-extensions (backwards-compatible jpeg->jxls vs pure-jxl). The former could be trivially handled with automated tools, but the latter can't.
AFAIK downconverting to jpeg is only an option for legacy jpegs that have been upconverted to jpegxl though. Many jpegxl images likely won't support downconverting if they were created as jxl from the get-go.
Basically, jpeg->jxl->jpeg is perfectly lossless conversion, but a newly-made jxl->jpeg is not, even if it doesn't use modern jxl-only features like alpha channels.
With that in mind I'd actually prefer if those were treated as separate file-formats with distinct file-extensions (backwards-compatible jpeg->jxls vs pure-jxl). The former could be trivially handled with automated tools, but the latter can't.