There aren't any fundamental issues with putting the git repo in Dropbox. Under normal circumstances, to cause a conflict you'd have to do something that writes to the git folder, then switch computers, pull up the same checkout, and do something else that writes to the git folder, all within less than half a minute.

The fundamental issue is that Dropbox changes are non-atomic w.r.t. what git considers "atoms." See my other comment in this thread. You're right that there's usually not a problem with a single contributor, but if you ever have two or more contributors sharing a Dropbox-contained repo it will be bad news.

Sure, don't share. But there's a good use case for putting a single-user checkout into Dropbox, and that's because it adds convenience and gives you continuous backups.