Piwik is a JS include, but it is on my own server. My statement wasn't accurate: I don't use third-party external hosted JS files.
Why? Security, privacy, performance. GA is probably relatively trustworthy in terms of security, but you never know. Privacy: Gone with GA. Performance: If the included library isn't far away, it's faster.
So, Piwik is good enough for me. I recently installed it on a VPS but from the same hoster in the same location. The performance is still slick, but a tiny bit of work is now off the server and security-wise it's better to have as few third-party libraries and applications running parallel to my web app.
The most limiting thing was that I rent a managed server that doesn't allow too many custom things. Piwik is relatively ineffective memory-wise in generating reports over months or years, if you have traffic like me (about 50K visitors per week or so).
The managed server would always kill the process, because it consumed too many resources and took too long. Never found a work-around. Now, on the VPS, I can do whatever I want and that helps.
This just as a warning if you're planning to run Piwik in an environment that might have limits in resource allocation.
Feature-wise, Piwik is totally perfect. As mentioned before, I don't track many metrics anyways. It's just a reference for keywords, which keywords converted, where people come from.