Do you mean that you would want that to happen on the web server, if they detect a user-agent that doesn't support JXL, they would convert back to JPEG? That seems pointlessly costly in CPU.
Also like mkl said, there doesn't seem to be any evidence that JXL->JPEG can be done losslessly.
Also like mkl said, there doesn't seem to be any evidence that JXL->JPEG can be done losslessly.