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Agreed. Why do the gaffes of some candidates alarm us so much? Because intuitively we recognize that dealing with the pressure of the presidency is imperative. Watching a candidate lose focus, lose concentration and panic during something as relatively benign as a series of debates is a signal to us that they don't have the intelligence or personality it takes to deal with life and death situations, or with our mortal enemies.
Absolutely. It's simply a hard and fast fact of human existence. People intuitively respond to the subtle intangibles in a person's voice and mannerisms on a gut level. Those with real leadership qualities emanate a certain kind of confidence and courage that strikes a chord in others. Such people ordinarily also have records of accomplishment that match what you experience while watching or listening to them.
Now, there are those who we might call con artists, or slicksters, who have an ability to so closely imitate the look and sound of a leader, that they fool some people. From my personal experience, it's mostly those who identify as liberals and Democrats who fall prey to this. Conservatives are far more discerning and observant, and can usually spot a trickster within the first few minutes of listening to them.
That group attribute bodes ill for any candidate who doesn't have real confidence and dynamic personal presence in a public setting.