Adding the GA tag would require a cookie notice and approval of the end-user.

I'm assuming this "requirement" is a legal requirement in some jurisdictions? The current implementation predates any such requirements and you are the first to bring this up. A PR which adds the notice is certainly welcome. Although, it would probably be best if analytics was broken out into a plugin. Then there could easily be analytics plugins for various services rather than only builtin support for one such service.

I agree with the opinion of plug-in. It's a feature that MkDocs doesn't necessarily need. I added to Wiki's Plugins Ideas:
https://github.com/mkdocs/mkdocs/wiki/Plugins-Ideas