No Comment has come to be the reply of all people who don't want to screw up and say the wrong thing while being interviewed. No Comment is used even if it seems more logical to say no comments. I guess the only place where I can think of that the words "no comments" are used is in the context of a sentence like "He had no comments about the murder" or when someone is ending an address "I have no further comments." "No Comment" would only be used when someone is replying to a question that he doesn't want to answer where he woud say "I have no comment."
Clearly I must always think I have more to say than no comment
Well, I suspect it is more that in my world we usually have the time for a longer sentence and would say the same thing in rather more words. No doubt my equivalent of No Comment takes five minutes or two pages. Training for public servants includes a week-long course (residential) on how to say absolutely nothing in a great many words, leaving the reader with the sense that all has been explained to him.