I’m educated in statistics too, but not to your level. I agree with your statements. I noticed something interesting at the worldometer cv site. Go to Colorado and hit the “projections” link on the far right.
Scroll down to daily deaths. You can compare Colorado’s rate of daily deaths to the other states on a graph. I was randomly doing this and was surprised at how often the smaller waves of rise and fall within the entire curve of Colorado would line up with different states’ small rises and falls within their larger curves. This happens even with some states that have much more severe curves and much larger case loads.
I’m not drawing any conclusions but I’m going to investigate that more.
I am guessing that they just took the curve of the flu or weather. And applied that curve to the projected curve of the corona virus. So they assume the same shape of the flu ongoing. If you see that pattern then you know they did not really model every state. Its one model and they apply each state’s data as though all the states are the same. Northern states are the same as southern states. Crowded states are the same as rural states, etc.