One instance of a time when action in politics was presented as a need over reflection is the No Child Left Behind law that was passed in merely a few months despite its being many, many pages. President George Bush was able to convince Ted Kennedy that the bill was worthy; won over, Kennedy gave his support, shephered the bill through the Senate, and the bill was passed. It was not long after its passage, that Kennedy changed his mind and withdrew his support of this bill--but too late.
This example is used merely to demonstrate how, given the time to read bills and think about all their ramifications may produce different results. There are many bills that congressmen have voted for without really knowing what is in them. Scary, indeed.
In a democratic setting, the need for political reflection is absolute. When this is surrendered and individuals stop thinking, the tendency is to have a body politic that is not entirely certain of the true story behind these facts and data that is being told by those in the position of power that wish to remain in power. When a citizenry "stops thinking" and places trust in the powers that be, the democratic order becomes more of an oligarchy, rule of the few. As you indicate, if the need for political reflection is supplanted by misguided action based on facts that reflect bias, government no longer becomes a democratic one, an entity reflecting the informed needs of the many. It is also the first step of power coming from "top down," and not, as the Framers might have intended, from the "bottom up." In the final analysis, I cannot help but feel that this becomes the ultimate reason why it is dangerous to "stop thinking" in a political sense of the term.
So as far as I can tell, your only question here is why thought is necessary in politics.
Political leaders are constantly having to make decisions that will affect the lives of many, many people. Therefore, it is very important for them to keep an open mind and not stop thinking. If a politician stops thinking, he or she will not be able to correctly evaluate the options that are available. Such a politician would get stuck thinking in one way and might not be able to change if the circumstances make it necessary.