1) You can go through the trouble of identifying and resolving all the edge cases that you encounter when using Git as a deployment tool. Keeping in mind that one of those may result in an embarrassing security disclosure. Woops.
2) You can use a deployment tool that was developed for that purpose, has existed for years, and has had many sets of eyes on it; many of which are inevitably more experienced than you. And you still may end up with an embarrassing security disclosure, but the chances are better that you'll hear about it through responsible disclosure channels first, rather than waking up at 3 AM to the voice of your boss/client asking why the site is redirecting users to buy Viagra at a discount.
A bonus third choice:
3) You look at existing deployment tools and ask yourself "I wonder why they do that?" Then, maybe ask around a bit. Once you've got a good idea of all idiosyncrasies involved with deploying software, then you embark upon building your own tool. I think you'll find that simply `git pull`ing from your httpd document root and `rm -R`ing the .git/ directory won't be your final solution.
The audit of commits in the general case (Checking for errors in the code) and the audit for the deployment case (Checking for sensitive data that may be exposed in a security breach) are different audits. I don't think many tend to do the second kind of audit.
Also, minimizing your exposure in case of a security issue is probably a good idea, so the convenience of deploying with git may or may not be worth this extra exposure.