> Our elected head of state would not be allowed to make decisions based on their own political opinions (much like a judge uses their power according to the law and the facts of the case, not letting their personal politics get in the way).

How do you judge the internal forum in that case? If the head of state says that they chose X because it is the right choice, but it's pretty clear to everyone that they wanted to choose X for personal political reasons, how do you prove it?

And if you have a method to prove it, why not use that method to arbitrate instead?