I can present to audiences pretty easily, I actually enjoy it. I also don't mind at all having a client watch what I'm doing. And yet, while I have no trouble doing interviews - having worked as a freelancer that would have been pretty bad - the situations are not comparable even for me. I
loathe interviews. Fortunately a lot of clients, and I've had several major companies, had people hiring me without any of the usual stuff based on a gut feeling, I had to answer silly irrelevant technical questions only twice. And once I even failed "explain a right join" - something surely everybody would be expected to know, and of course I do, but at that moment I blanked. I go the job anyway but it goes to show that even to me interviews are a very different and greater kind of stress than anything normal work can throw at me. Even if it
looks the same, it isn't, not at all! The brain knows context.
An interview situation is much more adversarial: They are looking out for reasons not to hire you, you are competing with others for the job and only one can get it! No such consideration on the job, unless the work environment is completely and ridiculously broken. When are you ever in a work situation where several people work on competing solutions and everybody else but the person who made the winning one is fired? At work you are working together, and to solve a problem, not to week you out of the pool.