the number of people who eventually get infected.

One way or another, an epidemic will evolve to the point of steady endemic infection or herd immunity for the population at large. One way to get there is massive levels of infection. The problem with that is more people will suffer the disease than is otherwise needed to get to a steady state. For disease with a non-trivial mortality rate, that also means more people die than otherwise needed.

In the absence of a vaccine, slowing the rate of infection through containment and social distancing is the right strategy.