An idea that just occurred to me.
All nations should be forced to grant citizenship on the basis of a Turing test. A group of certified-citizens are assigned to interview a person of unspecified citizenship.
If the citizens decide the interviewee shares their citizenship, that interviewee acquires their citizenship.
Only a few interviewee will actually be non-citizens. Citizens acting as interviewees are monetarily rewarded only if they convince the interviewers. Likewise, interviewers are only monetarily rewarded for positive-positives.
The point being, if a person cannot be distinguished from an actual citizen, there is no basis for denying them the right to reside and work in the country.
I haven't worked out details like the medium for interviews, off-limit questions, etc.
update: Please note, I am NOT suggesting this program replace other vectors for citizenship. This idea is strongly inspired by the experience of going to a US university and not being able to recognize some international-students as such beyond superficial qualities like an accent.
Consider this: say, Tesla applies for citizenship in, say, US. He has a brilliant mind, his ideas are awesome and very advanced. He is denied because he can easily be differentiated from the other people. If nothing else, then on the fact he doesn't know all the culture, the in-jokes etc. His life-dream is also providing free electricity for everyone.
Another scenario: Ada Lovelace applies for citizenship pretty much anywhere in her era. She is denied because she's all about doing the same things as men and not quietly making dinner and staying in the kitchen.
What I'm trying to say is that your idea would result in very uninteresting nations that would be completely intolerant of anyone standing out from the herd. Even moreso than they are now.