Anonymous identities are cheap. Suppose you are running a wiki, and are having a problem with spammers, trolls, and other abusive people. Now you can of course ban accounts for abuse, but this is the internet, creating a new account is trivial. This is especially true when you want to allow anonymous use of your wiki. (or for that matter, any service) Of course you can try to make it harder to make a replacement account with efforts like captchas and requiring email addresses from well-known domains, but these solutions all have drawbacks, and are often surprisingly easy for spammers and trolls to defeat. (you can hire humans to solve captchas for you at remarkably low rates)
Fundementally all those solutions are making an identity more expensive to get. Of course, you could just charge membership fees - Something Awful, 4chan and the Bitcoin Wiki all do this - but now you're running a business and users have to pay fees for every wiki they join. What you really want is some sort of way to value that identity that scales accross multiple sites and multiple contexts.
Suppose you want to start a micro-transaction service. You'll hold people's Bitcoin deposits on their behalf, and use efficient, centralized accounting to allow your users to make tiny, a few cents at a time, transactions. The Bitcoin network has a fixed, limited, capacity in terms of transactions per second, and as Bitcoin becomes more popular micro-transactions will inevitably be crowded out by fee-paying transactions for more significant amounts of money. At the same time, if the risk of that central microtransactions system going bust, or stealing all the funds, is low enough it will be acceptable to trust it even if you might not buy your house with the service.