Testing is not a panacea. No matter how much testing you do, you can't catch them all. How do you test homeless people, for example, who don't have fixed addresses and often don't want to be found while engaging in behaviors that often contribute to the spread of disease? Or people who live in remote areas and don't even want to be found?
The biggest problem in the US is that all tests had to be run through the CDC.
https://www.kqed.org/news/11806695/coronavirus-report-why-did-it-take-so-long-to-get-rapid-test-kits When you have a single choke point like that, you greatly restrict the ability to do massive testing. Now that testing has been authorized for private and public labs, testing will greatly increase. But think about it. If you test me today, I'll be negative. If I encounter an asymptomatic person tomorrow and contract the disease, I won't test positive for several days. What are you going to do? Test 327 million people daily? It's not even logistically possible.
Look at South Korea, the country that everyone is praising for their testing program.
https://www.voanews.com/science-hea...h-korea-britain-aggressively-test-coronavirus 105,379 people have been tested. 4,212 tested positive. South Korea's population is 53,732,586.
https://all-populations.com/en/kr/population-of-the-republic-of-korea.html So, they've tested 0.2% of their population, and of the people that they've tested 4% have tested positive. Yet everyone is praising them for their high testing rate. 99.8% of the population hasn't even been tested!
ISTM, the most efficient way to detect the disease is through testing of sick people followed by aggressive contact-tracing, as Indonesia has been doing and is what the CDC began doing early on. Massive testing may make you
feel more secure, but it's really not a cost-effective way to track down infections. But that contact tracing has to keep in mind that people will be asymptomatic for the first few days and may not test positive immediately. That's why the 14-day quarantine makes sense. If they don't test positive after 14 days in quarantine, they're likely not infected.
While it's true that "under testing" will miss cases of infection, overtesting isn't going to get rid of the virus. All it will do is improve the numbers, as South Korea has proven.