You'd miss out on all the goodies of version control like seeing what has changed. Ideally, version control for musicians would have the ability to show "change panning of guitar a to 0.3 and volume to 0.1" similarly to a code diff. Otherwise all you've got is just a bunch of backups, possibly with semi-informative commit messages if you really put a lot of effort into it.
I wish that there was a way of getting Logic X to output a list of changes you've made during a session. When I collaborate with my bandmate, I often struggle to describe all the changes I've made since he passed me the project. I'd also like to know the changes he's made.
My bandmate often works on our project while it's in a Dropbox folder, so I get a steady stream of notifications about impulse responses and undo files being changed; not very useful. I can tell when he's tracking because the new .aif files come over but that's about it.
I mean, Adobe Suite programs have a history feature where all your alterations to the image are listed chronologically. I don't know how that system works personally but it is a similar class of application & feature.