Most apps aren't built to use it, especially on mobile. Think of the use case of your grocery list--you want one tap, open the list, type type type, and done. Anything else--having to tap save, sync, write a commit message, etc... anything, is a fail in my opinion. Git is great to use behind the scenes but I don't want to see it in the UI or slow down my workflow.
Indeed, this can be done, but usually isn't. And when it is done, it looks like another proprietary syncing protocol.
The thing is that you should not expect a user to explicitly host a git repo somewhere to for a grocery list app. Most apps are designed for users who are unwilling to do that, and are actually ready to pay to avoid whatever technical hurdles.
OTOH I see a niche for an app geared towards more technical users, chich would, among other things, allow you to point at a git / hg / whatever repo to use as the synchronization point.
