"Everyone stop moving around for a few days so we can contact trace and test these people without it spreading more" seems like a very good mitigation.
It has worked well for NZ thus far; they've been able to demask, hug, and live life pretty much normally for a while now.
I'd happily take the occasional few days hard lockdown in exchange for that.
You have to consider what would happen otherwise. If you lock down cities at 1000 infections then how many other cities manage to reach 1000 infections before you take action?