Why haven't we hosted research publications as repositories yet?
There are journals that do that. Here is one: https://joss.readthedocs.io/en/latest/submitting.html

In some sense, arXiv.org is also doing that, allowing to version preprints. It doesn't use a "repository" in the sense of git or subversion, but it allows you to keep track of different versions of a manuscript, and that's really what is key: Any system that allows you what's in a paper at a later time must allow identifying and accessing a particular version of the paper.