How does this idea square with elections in the United States? Consider pollsters; their job is to make specific predictions based on understood methods using data gathered with also understood methods.
Despite what was either fraud or tremendous incompetence in the last Presidential election cycle on the part of ideological pollsters, and the high degree of public attention paid to it, polarization has not meaningfully decreased in any way I can observe.
I therefore expect that making the candidates generate specific predictions would have little overall effect on polarization.
The prediction expert Philip Tetlock writes in New York Times on the power of precise predictions to counter political polarization. Note the similarity to Robin Hanson's futarchy idea.