Not if they stay home
If everyone was out in public, then yes, everyone would become infected very quickly. That's why governments are telling people to stay home. If we can isolate people to slow down the spread, more people can be saved by limiting the demand on our health resources at any one time.
The growth is only exponential if you don’t slow it down by staying home. The exponential growth is only what happens if you do nothing.
I agree with all of this, but then that would also mean the “peak” is further away- or maybe we are using that word differently? Flatten the curve prolongs the infections so it either peaks fast with an expontial curve (and all heck breaks lose) or we prolong it (good for outcomes) but the peak takes much longer....
are we just using peak differently? Peak to me is when half the country has contracted it.