It's not a "pretty good solution", which shows if you start breaking down how you would attempt to achieve this. How do you, first of all, "remove diplomas"? Do you suggest that we fundamentally overturn how our entire society works just to remove cheating?
A "diploma", "certification" or whatever you want to call it, can be issued by many different entities: a collection of nation-states, a state itself, non- and for-profit organizations, even individuals. These all have varying degrees of value depending on the trust placed in the issuing body, from a certificate of having completed Bob's Weekend Sales Course to a state-issued certificate to perform a specific type of surgery.
First of all, which of these are you saying should be "removed"? Only the ones from universities? All of them?
Secondly, how do you remove them? Do you outlaw them?
Thirdly, what happens when they're all gone? How do you certify a surgeon?