It's great that the Ethereum community is increasing its focus on privacy. Not only because users in all likelihood prefer privacy but because it is simply impossible for money to be good money if it has public history built into it.

The best kind of money is identical in all meaningful sense but the money's history makes it unique and this is precisely what you don't want. What happens if you get money from someone and it turns out that those coins have been in touch with an adress way back that someone doesn't want to associate with for some reason? Institutions say "Sorry these coins no good to us. We don't want them.". Those coins are less useful than you thought and worth less than the "market price" to everyone because of their history. 

So you - and everyone else - must check if the coin's history is acceptable. But even if you do this it might afterwards emerge that an address you've transacted with has dubious connection way back - which you couldn't now at the time - and now you are burnt.