It's just like with GSM IMEI, notably pre-paid GSM cards, they're identified (in most countries), by an ID card when you buy the pre-paid card. If people wanted anonymity, they'd have to swap their pre-paid card randomly and anonymously in the street.
If you want anonymity with bitcoins, you will have to swap them on paper, in the street.
And even having shuffled bitcoins, you'd have to be very careful, because there are other ways to identify entities, based on their behavior. See for example:
https://hal.archives-ouvertes.fr/file/index/docid/718763/fil...
http://homepages.laas.fr/mkilliji/docs/journals/jcss.pdf
http://www.cl.cam.ac.uk/~ks640/files/papers/wpes2014.pdf
etc.
There are only 9 billion humans. Therefore to identify one, you only need 34 bits! Extracting the right 34 bit of information from the petabytes available each second, while requiring some mathematical and computing resources, is clearly not impossible.
Beware also of the Air Force 1 effect: when the American secret services destroyed the World Trade Center, they issued an order to ground all airplanes. All, but one, Air Force One. And therefore everybody knew where it was, because it was the only plane in the sky keeping signaling meteorological data.
Similarly, when everybody is tracked on facebook, on ApplePay and on bitcoin (however anonymously), getting outside of those tracking system only serves to flag and identify your even better!
We're certainly very close to have a system like in Minority Report, where not only real-time tracking of everybody will be relatively easy, but of course, probabilistic prevision of (near) future behavior will be possible as well.
When you can track with a high resolution spy satellite or drone somebody in downtown Los Angeles at 11:43, you can predict with quite a certainty that he won't be in New York at 11:50. Given physical constraints and Bayes statistics, you can predict quite a lot.
http://www.dailymail.co.uk/sciencetech/article-2269563/The-U...