I'm not sure you've understood the context of when people use this phrase fully. People use it when they simply don't want to respond to a question . This could be someone being asked an awkward question by a journalist, for example. The most typical use of this phrase, at least in the UK, is when a person is being interviewed by the police and they do not want to say anything that may implicate themselves criminally. In fact if a person does this they they are said to give a 'no comment interview.'

You say 'no comment" when you do not want to reveal what you actually think about something , so you will not cause any embarressment when the truth will hurt someone( rather than lying to make the person happy) or when you do not want to make your opinion known about something because you dont want to get involved

"No comment" is a stereotyped phrase a public figure uses when he chooses not to answer a reporter's question. He can't remain silent or the reporter will just keep asking the question. "No comment" is about the shortest possible way to phrase the refusal, and it cuts off follow-up questions. If he says "I won't answer," it invites the follow-up question "Why not?"