Maybe it's useful for a hardware wallet setup? Currently hardware wallets just flash the address on screen and usually there isn't enough room for the complete address, so it the user has to read some scrolling ticker made of random characters and "spot the difference". A hardware wallet showing the true fingerprint on the screen and the user confirming it's the same one they wanted to use could be a cool feature.
Sure, that's one use-case. There are many others. Once LN is up and running, Bitcoin payments can be manually sent over email and this makes the old-school "pubkey fingerprint" verification of a transactor's identity useful - if I trust you, I only need to know I'm talking to
you. A visual hash is a way to represent an abstract identity (your pubkey fingerprint) so that I know I'm transacting with you and not somebody else. You could argue that real-world identities are superior but sometimes I want to transact with people without necessarily breaking anonymity. In short, I can trust you (by reputation or imputation) without knowing any identifying information beyond your pubkey fingerprint. Visual fingerprinting is way more reliable for use with my working memory than strings of ASCII characters because the visual features in an intricate fractal pattern are instantly distinguishable, requiring no memorization. Strings of characters are more absolute but require memorization.
ATM, I'm playing with the idea of something like this,
http://mandalacreator.com/ but driven by something like an L-system (or a Markov algorithm) that takes input from a hash function.