On the bad side, some people get infected on the down slope too (when Reff < 1), causing overshoot. This is why even if herd immunity from recovered cases is unavoidable, it's important to slow the spread as much as possible.
But on the good side, not everyone has the same number of contacts--some people (police, medical workers, shop clerks, etc.) have a lot more opportunity to both acquire and transmit the virus than others. These people will be infected first and will recover first, providing disproportionate herd immunity. This paper attempts to model that.