We too have been a very satisfied Cloudflare user.
Although analytics is not the reason we use Cloudflare, it's interesting to note that in their new analytics, the primary metric for measuring traffic has changed from page views to requests. Since Cloudflare is the source of serving the pages, it seems like it would have the greatest opportunity for capturing accurate pageview counts. I wonder what the story is behind the change.
Any client-side analytics you set up by hand would have a greater opportunity for capturing accurate pageview counts. A proxy or host like Cloudflare can only guess, based on things like content-type headers and file extensions, which requests are page views. Most requests are not; they're resources needed to build the page like images and stylesheets, AJAX responses, API requests, etc. A copy of Google Analytics you put into a header/footer template, so it only gets served once per page when actual clients load a whole page, has a better idea of how many page views are happening.
This is actually the reason why CloudFlare has better analytics. Their system is more advanced than a regular reverse proxy and they can tell what requests are actually pageviews based on the HTML loaded.
Client-side stuff is unreliable and is open to everything from javascript blockers to network connections in the middle. CloudFlare even had a post about how their tracking was better (cant find it now).
EDIT: Yes I know newer ajax sites are completely different and there's probably no perfectly accurate way to track them unless the devs setup analytics properly, and even then its up to the same issues all client-side tracking faces.
Although analytics is not the reason we use Cloudflare, it's interesting to note that in their new analytics, the primary metric for measuring traffic has changed from page views to requests. Since Cloudflare is the source of serving the pages, it seems like it would have the greatest opportunity for capturing accurate pageview counts. I wonder what the story is behind the change.