While correct in the sense of word and versioning via mail being a nightmare, I really don't think you can expect anyone to learn latex just so they can comment in your document. I would have offered to send a pdf. Shoot me.

Still better than using file names.

But better for LaTeX

Git is a tool that makes it convenient and lightweight to keep past snapshots of a directory of text files (called a repository) and compare them. It also makes it easy to have multiple people work in parallel on the content of the directory, see the differences and merge everything into a common version. It is essential in programming, it's called versioning or version control.
Although it is not easy to access for non programmers because it's based on slightly obscure command lines. So it's a bit of an over-engineering to use it for a single file edited by a single person. Especially because you can now put those on the cloud and have some form of version control that allows to easily compare and go back to previous versions graphically.
It may be worth it if it's a long document that you work upon for a long time, such as a PhD thesis.