PostHog Analytics [1] is open source, and sofar a very nice alternative (or complement) to Google Analytics.

It's more like Heap Analytics, in that it collects user clicks and other events from your site (or app) and allows you to retro-actively define "actions" based on these events.

For instance, if you decide today to keep track of how many users click your sign-up button on page X, PostHog can graph this metric for you for every moment since you first installed it on your site.

You can combine actions into funnels, graph nearly everything, the GDPR support is first-class, there's support for heatmaps, feature flags (rolling out new features to just a percentage of your visitors), and user cohort analysis.

[1] https://posthog.com/

Free is a big part of the problem. The existence of free tools in a space, that are paid for with data gathering, crowds out the market for paid competitors that operate in a more privacy friendly manner.

GoatCounter is open source and there’s a free hosted option for non commercial use:

https://www.goatcounter.com/

plausible is open source (https://plausible.io/open-source-website-analytics) and can be self-hosted.

You can have a look at https://ownstats.cloud if you happen to have a AWS account available