Interesting. Fundamentally, I believe CAPTCHA, and attempting to distinguish humans from computers is pointless. I think it's better just accept it and design applications accordingly.
Avoiding DDoSability of your app (removing bottlenecks, scaling up replicas, implementing rate-limiting, etc). There are probably some rare cases where captcha is useful, though. For example some account creations where you wish to have more human accounts created, especially if you need to later manually approve them by humans (verifying documents, etc) and don't want to deal with thousands of cat photos instead of passport scans.
A reputation system that grew from captcha and was eventually self referencing - so high rep IPS could vouch for other unknowns. Assumes most people's IPS remain static though.
I realise parent commenter was probably talking about identifying upfront.