If the client is somewhat technical, and doesn't mind mucking around in markdown and the occasional html then sure, why not? But most of my clients prefer having a simple to use backend for updating the site.
Depends what you mean by "static" at this point. I've created sites that were updated infrequently, and so I wrote a script to build out a static mirror of the site after updating. By exposing only the static mirror you get the best of both worlds. For a higher end setup, you can run a static caching layer on the HTTP server netting you the same performance benefits but without manually building the mirrored version.
Will be interesting to see when the next generation of "content APIs" hit - client updates a field in a backend somewhere and it rolls out to static sites, apps, bots etc... all over.