That is a grey area at best.

For one thing, a cookie that has a dual purpose, controlling both logging in and analytics, appears to give up any exemption on the grounds of strict necessity that a cookie used only for logging in would be granted. You would probably be required to provide all kinds of explicit information about your use of the cookie to anyone before allowing them to log in and setting that cookie, adding at least one extra step to your sign-up process (or making use of a single sign-in service much less convenient for your visitors).

For another thing, that still restricts your analytics to cases where someone is already logged in or otherwise actively using your site. Often the more interesting things to know relate to visitors to your site who are not (yet) so active: what are your best traffic sources/keywords, where do new people come into your site and where do they go next, and where do they give up if they don't convert?

You don't see how this is a major pain?

You can already get this behavior in your browser by changing user settings. Just try to surf like that for a while. It's horrendous, and what's worse, it doesn't make the user any wiser, really.