By simply using the scientific method, it doesn't mean you have to abide by it regardless of the ethical consequences - what a frankly stupid thing to suggest.
It identifies the best method, then our ethical rules are applied to ensure no breaches of human rights are observed.
Which then undermines your "evidence based approach" if we are disregarding any evidence for whatever ethical reasons we decide upon. It also doesn't address the areas where scientific evidence is only partly or loosely available. (Which you asked for examples of and then completely ignored for some reason).
What part of using the scientific method to determine the validity of a claim means using whatever method is optimal 100% without any external considerations?.
I'm struggling to see what point you are trying (and failing) to make.
The point I am trying (and obviously failing) to make is that your ideal of an evidence based approach is flawed in its own way because a lot of the problems dealt with in the political area are not currently modelled to any real degree of accuracy.
Obviously, that doesn't fit with your ideology..