So, the "test our way out" strategy wouldn't be for the purpose of tracking individuals, locking them down, tracing their contacts then locking them down. That's just not viable outside of pocket regions (mostly cities). The US is too distributed. Too large. People are complying voluntarily now, but implement SK's measures on enough people for a long enough time, in some cases interfering with essential matters of survival and they'll stop. China, with all its tech surveillance and draconian measures, never gave a thought to trying to also carpet bomb the hinterlands with bleach. They never sent the PLA to patrol the boonies for violators and drop off rations once a week, as it did in Wuhan for months. Because they couldn't have. Distributing resources would have been beyond them, (let alone trying to enforce anything).
The purpose of mass testing is to
get an idea of where Covid is and what it actually does.
We are presently working off equations that are using nearly blind guesses to populate almost every variable in them. The only thing we know for certain is that high population density + mass transit + covid = bad. How bad? How high can a pop density be before covid creates real disaster? What needs to be the rate of mass transit usage? We don't know any of this.
Obviously, an accurate test is better, but
even an inaccurate test could, for example, provide a better estimate of R0 than "somewhere between 2 and 35." An inaccurate test could give you a better prediction of estimated total US covid mortality than "between 30k and 2 million."
We don't need a vaccine to proceed from where we are to something better. But before we can do that, we need to know
1. how quickly covid spreads
on a per region basis, both in quarantine conditions and without them
2. what the rate of hospitalization is per infection (this should be static once adjusted for demographics)
3. a better guess at the true percentage of people who have contracted covid at some point
The testing doesn't need to be accurate to allow for improvements; it just needs to be granular to the region and better than the little that we have now. Even with a test that has a 30% error ratio, we could narrow these variables down a lot.