I think the main benefit is that a scientist elected to a political office would make decisions based on real data when possible. Obviously it is often times not possible - for example, you can't use science to determine whether you should take a pro-life stance or a pro-choice stance - but the insistence on using numbers would greatly simplify many decisions.
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If a scientist made decisions based on real data, wouldn't they conclude that the approach used by the current politicians is superior for the purposes of politics?
The data says it works, after all.
Totally agree. There are benefits that a scientific stance would have in some circumstances, so it's a nuanced situation. :)