This is a useless bit of pedantry. The exponential portion of the sigmoid curve is the only part that matters to human health, survival, and economic well-being.
Epidemics are (more) properly modelled by the Gompertz function[1], and the position of the "transition" between the exponential portion and non-exponential points it the important point.
That is exactly what the person you are replying to is saying ("they always break into some other curve at some point.").
Is the Gompertz function the function behind the standard "epi curve"? It appears from the CDC web site and other places that the epi curve is the standard way epidemics are modeled. The CDC even has a simple tutorial for creating them: https://www.cdc.gov/training/quicklearns/createepi/index.htm...
You and I must be thinking of different professionals.
At any rate, here are two very very very simple models of this epidemic: a) cases will grow linearly, b) cases will grow exponentially.
Super simple. extremely different outcome. Now, one still has to make policy decisions.
I think the solution is not fewer professionals, but more and better professionals.