I would love to agree with you but this isn't just a politician thing. It's an intelligence measure in practically all walks of life. Any interviewer, manager, or even an acquaintance at a social gathering would judge people the same way.
It's definitely not that overrated and it's not just a skill of quick thinking and wit but more of a combination of things like being well-educated and interested in knowledge, being prepared, "social" intelligence in form of empathy and perceptiveness and respecting your audience etc. Actually having values also helps. When you are straight up BS'ing people, intelligent and knowledgeable people will see right trough that and then likely to view you as dishonest and insincere or even dangerous. So it's not that good of a bet as often as is generally thought. People like that poor girl in the video usually generate plenty of sympathy even if they might be seen as dumb. One of my pet peeves (and the reason why I bothered to stop my usual lurking) is that education is also often seen only as a "tool to make more money" which is in my opinion very saddening and even infuriating. That view tends to make otherwise very competent people put feet in their mouths when faced with questions out of their narrow comfort zone. The former is also one of the less obvious reasons why "idiots" with high socioeconomic backgrounds do better than they should since they are likely to understand the social games better than their counterparts not because of their academic excellence or measurable intelligence but because their upbringing usually has put more value than the average on things I mentioned earlier. Of course you also have the "Romney-type" who despite all the advantages they have had, often seem to perform like the girl in the video and garner no sympathy at all. As for politics, most people probably shouldn't be allowed to vote anyway so you have a point there. And yes, would hit.
