But one requirement of a captcha system is that it be easy for a computer to generate. The system you describe seems to require that humans build up a list of things with obvious-to-human answers, which doesn't scale, especially when they have to be designed under the assumption that "the enemy knows the system" (i.e. a worker on some "library of common knowledge" project could defect).

But if you could have an AI generate those problems, it would be capable of solving them too!

Current captcha systems exploit the one-way nature of problems, mainly "character distortion". This is what permits easy computer-generation but not computer-solution, and does not seem to be present in the class of problems you describe: it's just as easy to go from "noun -> adjective" as "adjective -> noun".