I Have a Question About “Flattening the Curve”

I’m puzzled by something. A few weeks ago, before we had adopted any social distancing measures, the COVID-19 models suggested that we’d hit a peak of 5,000+ deaths per day sometime in late April or early May. Then, in mid-March, we started adopting countermeasures. Famously, these countermeasures were supposed to “flatten the curve.”
As you can see, countermeasures were supposed to lower the peak number of deaths but push the peak outward. The total number of deaths would stay roughly the same.
But that isn’t what’s happened. The peak has been pulled forward and the total number of deaths has been cut by two-thirds or more. What’s going on here? What am I missing?