In short: It's flattening the curve, not shrinking the area under the curve. The better we do it, the longer it will take.
P.S. Since this is inevitably political: in my personal experience the misconception that "the better we do it the sooner we can stop" is being spread by liberal/lefty people who are in favor of strict social distancing for as long as it takes. I think they're trying to rally enthusiasm for compliance, but the fact that this optimistic spin coincides with the political rhetoric from certain conservative ideologues should give them pause. Some politicians are anticipating and subtly fomenting a loss of patience with social distancing, and anything that raises unrealistic expectations plays right into their hands.