While the extreme "master of one" exists, most academics I know have cross-cutting interests.
We also shouldn't forget that the vast majority of politicians today are lawyers by education. To whatever degree your assumption holds, it is true of the status quo today as well. Even in that case, having a more diverse set of "masters of one" would be an improvement.
Slight correction (can't edit): law education is most common for politicians in Western countries, but not the majority.
For the US, 32% of the house and 47% of the senate holds a law degree.
I was only addressing what "overeducated" refers to. Politicians of western democracies I know of have the problem that each leader is afraid to surround himself with people more capable than themselves, for the people around him are competitors for his position.
Unfortunately, eventually one of the people selected for being less capable get to be at the top and continue the whole play again, getting rid of anyone that is not less capable than themselves.
This is one disadvantage democracies have over monarchies, for a king can surround himself with more capable people all he wants as they are not direct competitors.