Serve the static files from something that can handle it, sticking nginx in front of apache as a reverse proxy works well here and will both catch whole pages (once configured for it) and serve all those pesky CSS, js and image files directly so apache doesn't have to.

Letting the php app server (apache in most wordpress cases) handle things it shouldnt is the real issue here, everytime apache has to serve a static file, that worker process can't render or even serve cached pages.