It is used commonly with facebook groups. Having to answer a question related to the group topic filters out spammers. I do it for country specific country sites requiring knowledge. The information can be googled if desire is high.
Facebook groups I can see, especially because they're often surrounding specific niche topics that you can reasonably expect people to have some shared knowledge of, and the administrator of a Facebook group doesn't have that many levers to pull to reduce spam.
At the country level (and for applications where you have enough control over your infrastructure to use a real firewall) I question both the efficacy and accessibility of a system like you propose—it's not that different from the old style "what is 2+2" CAPTCHAs, and there's a good reason why most applications have moved on from those. They're not a serious alternative to behavioral rules like what OP describes.
