Why does CAPTCHA exist? To prevent bots from using our site.
Why don't we want bots to use our site? Because their output is worth less than our site's resources.
The real purpose of CAPTCHA is to limit our expenditure of resources and improve the quality of data flowing into our site. Contemporary bots tend to produce low-quality, high-volume output while your average human tends to produce output of sufficiently high quality.
Consider a hypothetical bot that was capable of producing input to our system of sufficient quality. Would we want them included or excluded from participation?
As has been argue before, we realize one must be judged not on by the color of our skin, but the characters of our content.
By adopting such a stance we can then see that we are fighting a battle over input quality. It is our goal to improve the signal-to-noise ratio of our system's content by making it difficult for any party to contribute "noise".
We then see that a successful implementation to solve this problem will also help solve the related problem of "trolls" and "trolling", whereby humans intentionally post provocative messages in an attempt to provoke a reaction and derail legitimate discussion. This problem can be recognized as a different case of the same problem as bot-spam.
Several successful methods of this type exist such as Bayesian spam filtering and karma voting systems.
I'd like to see it taken further: natural language processing, categorization, etc. Conversation/Argumentative meta-data. Pattern-matching. Comment consolidation and refactoring. Auto-summarization.
What I'd like to see is sites accept input from any and all sources and incorporate the source's status, as well as the content into the content's use.
CAPTCHA is a stopgap measure trying to defend against a special case of the real issue: quality input. Define quality and quality will rise.