A .tar archive is basically only the files cat’ed together, with a header and index added, right?
And a .tar.gz takes forever to modify, because it needs to first extract the .tar.
So why is there no archive format that just cat’es the compressed files together?


TAR is short for Tape ARchive. It was originally meant to be written to magnetic tapes. Like cassette tapes. As such they are not really meant to be changed much. You read the whole thing from beginning to end until you find what you’re looking for.
Modifying it would usually mean writing the whole thing again. So that is more a modern notion.