Exponential growth doesn't seem like a problem, until it is. A primary concern is reducing peak load on medical services.
1. Reducing the transmission rate lowers the total number of people sick at one time. Lowers the ultimate number who contract it. And pushes the peak infection rate out.
2. The above numbers are very sensitive to r0.
3. An exponential when it hits looks like a wall. You end up with a significant percentage of the population sick at once.
Could be my model being shitty but it looks like at high r0 there is a momentum effect which drives the total number infected above what you would expect.
Note this is a “mean-field” model (everyone evenly mixed together) so take it with a grain of salt...