I realize the use case, but since addresses are single use, what would you be looking for when seeing a new fingerprint?  I agree about the usefulness in the "receive new address now, send coins to it later" case, but it's limited to a person's memory, and it's still possible to misremember some minute features of the fingerprint.
After long use of the same fingerprint you might begin to distinguish it better from others that are similar to it, but that's no good since it means you're just re-using addresses, and in case where some malware intentionally replaces addresses in your clipboard with some different address that might normally change the fingerprint, the same malware could replace the fingerprint too to show what would be the "honest address's" fingerprint.

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.