Look, I will give you just one example. Look at the mess with the Ashley Madison. Imagine if their users had an opportunity to pay in Bitcoin by staying anonymous or even semi-anonymous. I am sure many of them would choose this option.
Bitcoin can have many use cases like this one in the adult and porn industry, meeting and dating websites, etc. And I am sure it will have after the Ashley hack.
The question is, Will Bitcoin give them more anonymity? If the user go through a 3rd party payment processor, he is still doing the same thing he would have been doing, using a credit card for payment. Bitcoin is only pseudo-anonymous, if you use it in the correct manner.
It still gives you the better option, if you do some home work. ^hmf^
That's why you should mix your coins in order to gain even more anonymity. 100% anonymity isn't possible, but you can "clean" your coins and then spend them on whatever thing/service you want. I always mix my coins before sending them to my cold wallets and even before spending them.