There are two primary issues here: the prevalence of Google Analytics and the unencrypted nature of the majority of websites. Google Analytics is on a substantial proportion of the Internet. 65% of the top 10k sites, 63.9% of the top 100k, and 50.5% of the top million[1]. My own partial results from a research project I'm doing using Common Crawl estimates approximately 39.7% of the 535 million pages processed so far…
First, as pointed out, you "cannot track a unique visitor across the web using GA cookies" because of the way they're designed: https://news.ycombinator.com/reply?id=6889120&whence=item%3f...
Second, the NSA doc as excerpted in the WashPost article talks only about Google's PREF cookie, which is set only when you go to say Google.com, not when you go to a non-Google property. It's a first-party cookie used for things like saving language preferences when you're not logged in, not for advertising across other properites. (That's what the Doubleclick cookie is for.)