so, these graphs where they normalize different cities or countries based on a number of days since the first known case, or since the first known death...

i wouldn't take them very seriously, in terms of actually comparing outcomes in different regions.

1) the decision to plot these graphs was taken back when we thought r-not was much smaller than we know it is now. we also thought the virus was much more deadly than we know it is now.
2) we now know that the virus was circulating in highly connected regions months before we really detected it, so the starting dates are very hard to pin with any accuracy.
3) as we've received more data about who the disease affects, the disparities have just become greater.

so, in city a, the first person that caught the disease might have come in contact with an elderly person within hours, and that elderly person may have died a fast and miserable death. if the first person is quickly isolated, that might be the end of that vector altogether.

on the other hand, the first person that caught the disease in city b may have flown in to the city to see a concert populated by teenagers, who then infected their relatively young and healthy parents. it could in theory take weeks or months for any sort of mortality to develop, and in the process you could see thousands or tens of thousands of cases.

these are extreme opposite scenarios, but it gets the point across - the metric is actually really not very standardized at all, and lining these curves up on top of each other based on it could very well lead to some very wrong conclusions about how the disease is spreading in any particular place.

you might be able to salvage the concept if you shift the alignment to a more advanced point in the curve, but it seems to me that this would mostly undo what people want to see, which is what's happening in early stages of transmission. really, this is a tool of analysis that should only be employed after the fact, and by lining the different cities up at their respective peaks. that would help us understand what already happened, but wouldn't help us predict the future.

a better idea to understand how the curve is growing is to dispense with the visual comparison and just rely on some basic calculus. after fitting the data to an equation, what is the derivative of that equation? how is the instantaneous rate of change evolving over time?