If you visit a web site the operators of that site will know that someone at your IP address visited the site, which pages you viewed, how long you lingered, which buttons you clicked, etc. If you want to prevent that your only option is to browse via things like proxies or Tor.

Why do you object to self-hosted analytics? I understand blocking centralized trackers (I do so myself), but self-hosted doesn't seem problematic in the same way GA being present on half the pages on the Internet is.

It also strikes me as an unwinnable battle for all but the largest sites.

Because OP is against all kind of tracking? And because he can...

I can't claim to speak for OP, but am also against most tracking. I would also tend to think that being against first party tracking would be an unwinnable battle. It also leaks less data than third-party tracking, since the third party can see your activity across multiple sites whereas first party can only see your activity on that site unless it's aggregated through a backend service (another poster mentioned the ability to upload server logs to GA). No matter what, they can see what you load from their site.

Getting to first party hosting of more intrusive analytics (scroll location, etc) I think rather than disallowing certain scripts/URLs to run, you have to get back to behavioral-based blocking. Doing that in an environment that you allow any JS to execute seems tough since sandboxing something that can update the page based on location can "talk" to another part that can report back to the server.

If you don't like intrusive first party analytics, just stop all JS.