Knowing what you bought isn't the only information that you can get from a transaction. For example, you could possibly discern:
- The transaction creator's salary. (If the inputs in a transaction came from your salary payment.) At the very least, you put a minimum on how much money they have.
- The transaction creator's location. Many websites track where payments come from, geographically.
- Where you buy things. If an onlooker has access to address information from one party, say Overstock for example, then they can see if you transact with them. And sometimes where you buy things is a strong indication of what you're buying.
So, knowing exactly what item you bought is not the only information that a user may be trying to keep private.
This strikes me as a exceptionally broad question. Anonymity from whom, and in what context? Take the OPM hack. None of the people exposed were criminals, but it still matters that that the 3PLA has all of that information on government employees. – Nick ODell – 2015-10-22T00:12:38.363
@NickODell, I think the title is not a great representation of what the OP is asking. I just changed it. – morsecoder – 2015-10-22T15:16:19.060