Re: Plenty of alternatives to GA
AWStats actually logs nothing - it does process your server logs to extract information. It has also a client-side script to gather some info that can't be provided by logs (screen size, etc.) - it's not mandatory.
It's lighter than an ELK stack and easier to install - one needs Perl though.
Just be aware of the data retention window - if one deletes the web server logs after a while, after they've been processed by AWStats, most of their data will be kept in the AWStats data files.