It is not that trivial, because there are tons of existing JPEG files and lossy recompression costs quality. (PNG does get replaced primarily because lossless WebP is kinda a superset of what PNG internally does.)
Just re-encode it to Jpeg XL without loss of quality, and use less space.
On your last point: I find it super annoying when both lossy and lossless codecs have the same name, and, more importantly, file extension. I get it that internally they are "almost the same thing", just with one extra step of discarding low-impact values, but when I see a PNG/FLAC file I know, that if the file was handled properly and wasn't produced by Windows clipboard or something, it is supposed to represent exactly the original data. When I see JPEG/MP3, I know that whatever it went through, it is not the original data for sure. When I see WEBP, I assume it's lossy, because it's just how it's used, and I cannot just convert all my PNG files to a newer format, because after that I won't be able to tell (easily) which is the original and which is not.