Dealing with basically another .webp-like format in those cases (one that might be a backwards-compatible jpeg or might not and determining that can only be done by inspecting the file contents) doesn't sound super fun.
So ideally, to make up names, I wish they'd used separate extensions and so a ".jp3" is a file that can be downconverted to a jpg and you could get a browser extension to automate that for you if you wanted, and a ".jxl" is the new file format that's functionally another ".webp"-like thing to deal with and all the pain-points that implies.
But like I said in my other comment (which got hidden for some reason), it should be noted that a recompressed JPEG is also a valid JXL on its own. If you have the means to turn a recompressed JPEG into the original, you also have the means to view native JXLs.
Hopefully adoption is widespread and we won't really have to worry about it. JPEG XL is a much more appealing format than WebP, and unlike WebP there are great arguments for software to support it other than "Google started using them, so they're everywhere now."