For me, the best Google analytics replacement has been nothing. Just don’t do analytics at all. Your web site will still work without it. In fact, it will work better!
It objectively won't.
Analytics tell you where your website isn't working, so you can fix it. Buttons you thought were obvious that users are blind to. Pages where nobody scrolls because they didn't realize there was more content. Figuring out where users get stuck because they don't understand the navigation you designed. Etc etc etc.
If you have a hobby website, then sure maybe analytics don't matter. But the idea that sites work better without analytics makes as much sense as saying you'll see better when you wear dark sunglasses.
What I am trying to say is that you can still do analytics, even pretty advanced stuff with some more elaborate scripting, if you want. The only thing you need is the access log.
Something which has been largely forgotten ever since tools like Urchin became a thing :)
Not a single line of tracking or analytics on the front end, we just tracked everything we cared about at the server level.
¹ To those who would say it doesn't matter, I'd say that laws aren't laws if they can't be enforced and there's no enforcement mechanism for some EU bureaucrat to fine a company with no operations outside of the US.
² I'm sure the technical means existed to do it especially if you already had access to the logs but the point is we weren't explicitly storing any PII or data that was linked to a real account. Just actions throughout the apps.
Urchin was acquired by Google and was ultimately sunset in favor of Google Analytics. It supported local and hybrid analytics models, the later arguably evolved into Google Analytics.
<source: did fancy things with logs over the last 25 years, including running multiple tools on the same site in parallel to do comparisons (Analog, AWStats Urchin, GA, Omniture, homegrown, etc...)>
For example, in the EU, you need user consent to use server logs that include IP addresses for analytics. You also need to provide post-consent opt-outs and privacy statements and audit logs and all off a sudden you're building another analytics tool.
This is sort of like assuming everyone who is taking photos at a tourist attraction is doing so to show off their holiday for social status.
If your site or content is truly valuable, it is a public good to monitor, analyze, and improve upon its reach and usability.
Maybe you're writing for an audience and you want to see what resonates most with them.
Sometimes popularity is a good thing to measure, not for your ego, but by how much you are helping others.
It is sad when people assume metrics are about vanity, rather than about how much we're helping others.
In my experience, when analytics and the related ads tracking tools break, Marketing departments are revealed to be much more important than generally believed in the business.
It helps run your business and make sure everything works as expected, and that you don't waste money on ads/marketing/seo/traffic, etc.