That is not a solution, apache/mod_perl/PerlMonks already keeps logs/stats -- all that would do is share them with google.
Yes we would be sharing data with google and all the gods would have to do is add a js snippet to the site templates. A small and fast change, easy. Furthermore, google analytics (GA) would give us access to all kinds of search related and end user related data that is not collected by web server software. So yes using GA is a valid solution to this kind of data problem. If your real concern is privacy that is a valid point, which is why I suggested an open source option that can be run locally as well.
I'm not sure how hard it would be, but all you have to do is persuade gods to share some awstats generated pages with you
The purpose of this post was to start a dialog with the gods, pmdev and the community about what stats can do for PM. I know there are plenty of other front and backend developers on PM who use web stats to make better things or are interested in the issue.