The whole point of citizenship is that it is a sort of legal contract of sorts between the would be citizen and the rest of the citizens. It's not a simple matter between two people.
If such a marketplace were to be legally implemented it should be far more complicated than a simple swap of citizenship between two people. Even then, the liquidity of citizenship would undermine its value, for better or worst.
If there is a marketplace then it's value will be determined by that market. If people can move into apartments and can be interviewed for it, the same could apply here. Obviously, I haven't thought this out completely and naturally there are all sorts of complications, but in reality, the question is - why can't people freely migrate from country to country? Naturally there are costs involved, a legal bearing, maybe even a quarantine timeline, but it should be possible. People did that all the time until the 20th century and therefore, it's an artificial barrier that's been put up.
If such a marketplace were to be legally implemented it should be far more complicated than a simple swap of citizenship between two people. Even then, the liquidity of citizenship would undermine its value, for better or worst.