Which part is improbable?
If the virus just traveled and conditions were equal throughout the country, then the plateau theory makes some sense. But during that time, here are just a few variables that have changed, and how I would have expected them to impact the number of new cases:
Increased testing - huge increase of new cases
Social distancing measures by businesses - decrease of new cases, with an increasingly greater impact throughout the 32 days
Availability of PPE - decrease of new cases
Stay-at-home regs - unknown, different states rolled out and rolled back regs a different times, definitely wouldn't expect it to average out perfectly
Moving hotspots - unknown, but given differentials in climates, demographics, population density, local regs, and mass transit usage, again definitely wouldn't expect it to average out perfectly
The range is within 5k, every day, for over a month. That stands out to me.