Get appendicitis? Routine surgery, can be done in a few hours. And will definitely kill you without treatment. Break a bone? Car crash? Treating you in emergency now might involve kicking someone else off respiratory support.
The cost of overburdening the healthcare system is not some calculation of a nuisance amount of citizen death over a time period - it's a whole bunch of people who otherwise live full and productive lives, instead stop existing.
What happens when you go above that dotted line is not the continuation of a predictable trend, it is a chaotic bifurcation in behavior which does not have predictable secondary effects. The COVID-19 case load follows that shape. The deaths and long-term health problems do not.