Yeah, let’s go door to door demanding blood. That will make for quite a spectacle.
You don’t actually need a massive sample size - 1000 random people would work. Better than destroying the world’s economy first.
There’s apparently a 15-minute test you can do at home for antibodies, already approved, used in China. If you had a choice of being locked up at home for 2 weeks, or giving a blood sample, you’d probably give the sample.
If they really have 40% of more already infected and over it, this means that the peak of the “worst case curve” is a LOT lower (both because it reduces the effective population by 40%, AND it also means 40% of your population is a barrier.
If you tell stores to prioritize immune people to cashiers and put the not-yet-immune in less public positions for a while, you achieve social distance at low cost.