I think for starters this would never happen in the current US both due to a lack of political will and highly varying circumstances (things were fine in Texas at the start, why would they lock down?). Not to even mention legal challenges. I believe people would need to be dropping dead nationwide to the tune of one in a hundred or thousand per week for this to happen here.
But even if we could I don't think it would save us for some of the following reasons, though it might have bought us a couple week or month reset. However, if this were followed up by strict adherence to social distancing, mask usage, and restrictions on social and work gatherings, we'd likely be in a much better place than we are now.
Completely eradicating the virus when there are tens of thousands or hundreds of thousands of cases seems unlikely to me. Enough cases are likely to persist through propagating within large households, cases with extended infectious time period (I'm not sure how likely this is? It seems to me like it should be possible for some cases to remain infections for longer than normal periodas of time, but I haven't read anything about this), and people not following the guidelines to give a sizable enough base for the virus to recuperate. And even if some areas do eliminate it, it can come back through domestic or international travel.