Is anyone using an open source statistics system that's as simple as simple analytics? Maybe even something that can be setup to run stats for multiple clients from our own VPS?

Shameless plug, but PostHog is MIT licensed, open source product analytics [0]. You can use it for super simple pageview analytics and even give all of your clients their own team on one instance.

If you want something more advanced, we're comparable in features to Amplitude or Mixpanel too, but more engineering focussed.

[0] https://github.com/posthog/posthog