Germany and Finland are doing this. Here are some results already completed in a German town showing that 14% of people tested positive for antibodies...
That study did their research in a town that was already infected, meaning that our understanding of the infection rate for Covid-19 is probably lower than reality.
Precisely - as an early outbreak centre that town is referred to as "Germany's Wuhan", and is expected to have among the highest proportion of infected inhabitants. So actually the 15% figure came as a disappointment and something of a surprise.
A disappointment? NYC has among the highest testing rates in the world and has only found about 1.5% of people infected. If there's another 14% in NYC that have been infected without needing medical attention, that is fantastic news.
The German town of Gangelt is the study case that the OP was referring to, which thanks to a small population and a well-attended carnival party with many infected attendees and a legion of subsequent linked cases had acquired the reputation that everyone must have been exposed, i.e. a place that would have established something like herd immunity. So to discover that only one in seven inhabitants had detectable antibodies was indeed dismaying: either the infection pattern or the immune response wasn't as expected. Or both.
https://spectator.us/covid-antibody-test-german-town-shows-1...