You make a good point of saying let it run it's course. Keep in mind the caveat of hospital capacity to handle the peak and also with higher numbers of infected the more variants will present.. I've found no data of age profile of hospitalizations and we know there are at least two strains with different manifestations.
Even running it's course there will be more than one returns of this virus.
It is right to attempt to limit the amount of infected at any given time and it's good to quickly develop a vaccine.