The whole "flatten the curve" messaging always seemed like we were barreling toward a misunderstanding, and I think this comment and the disagreeing downvotes are a perfect example of that.
Back when US public health messaging really went all-in on that phrase it was like late February when we thought the transmission level was minimal. "Flattening" the curve at a minimal level would have been fine, and if we got the reproduction rate even just barely below 1 the infection would have died out.
Flattening the curve when there are 10,000 people dying a week is a very different situation, and I don't think ending up there was ever explicitly anyone's goal (except for famously Sweden). But that's what we finally ended up achieving in April, and everyone basically patted themselves on the back for it and started treating the pandemic as over. It should have been very clear to anybody paying even a little bit of attention that once we started approaching and then surpassed "running out of ICU beds"-level of crisis in some places, that flattening the curve anywhere near that level would not be good, and when we did start to plateau at only like 30% down from the peaks we were nowhere near in the clear. But for whatever reason we just ignored that inconvenient fact and acted as if our lockdown had worked. After all, we had "flattened the curve".
Obviously the world is quite complicated and this is impossible to predict, but I genuinely wonder what would have happened if a more ambitious catchphrase had caught on instead like "zero out the curve". It's well-known that laypersons are naturally bad at reasoning about exponential growth, but I also think the public health "experts" really let us down as well in their failure to properly account for the exponential growth as well.