Actually, stuttering makes you look ridiculous and funny, and the listeners themselves are also embarrassed. Of course, a day later no one will remember your performance or interview, and for the most part, as you rightly point out, no one really cares, but you, at least in my case, and I can vouch for most stutterers in their cases, will remember everything, these micro-moments when you stuttered once again. The paradox of stuttering is that if you put all thoughts aside, you will actually stop stuttering (at most - slight prolongations), I have always had this experience with my speech therapist when I stutter enough, and I am sure I will have a similar experience with a group, with groups of people, if, again, you don't care about such things as time, their attitude, consequences, etc.). The problem is that it's an unacceptable luxury. I would agree to it perhaps if it was the first and last time I was seeing people, but embarrassing myself in front of people I've been seeing for years is too much.