"Those advocating for low case counts at all costs are basically advocating to close parts of public life for good."

This is not true. Once cases are low enough a competent government can prevent outbreaks from spinning out of control, as has been seen in South Korea, China, and even Australia where new outbreaks have happened but haven't lead to exponential growth.

The problem in the US is that the governments in many states, and certainly at the federal level, aren't even trying to a competent response and instead threw up their hands. That's why they're seeing exponential increase.

A several month lockdown is necessary to get cases low enough that a competent government response and protective measures can keep them low even with increased economic activity.