I suspect that Newt had a pretty good idea what the problem was likely to be, and he was in fact able to fix it very quickly. But if he hadn't started off by at least pretending to listen to the user's concerns (aka "waited until he'd run out of steam") the user would have felt ignored and it could easily have developed into a shouting match. Even if Newt had just ignored the user and fixed the immediate problem, the user would probably have been concentrating on his own rant rather than the solution, and nothing would have been gained.
Most people are easier to deal with when they feel that they've had their say, and are more likely to listen to what you have to say.
In a perfect world Newt wouldn't have had the last word in the way that he did, but we're all human.