Quarantine

As I understand it, the justification for citywide, statewide, or national lockdowns is to avoid exponential infection rates through curtailing physical contact in large social gatherings. A kind of preemptive quarantine measure. 

I'm no expert, but doesn't effective quarantine require identification and separation of the infected from the uninfected? 

By contrast, lockdowns are indiscriminate. They force families to say at home. Yet families are notoriously contagious. If one family member is infected, other family members are likely to become infected. So aren't lockdowns creating millions of family-size petri dishes where infected and uninfected are exposed to each other? Doesn't that cause the infection to spread exponentially, only it's temporarily hidden behind closed doors? But maybe I'm missing something.