They tested and keep testing everybody in South Korea because they were at a early stage of spreading. It's too late for countries where there are already thousands of cases. Tests at a larger scale in "infected countries" is a waste of time and people. People should just stay home and avoid any contact, that's how they can help hospitals to deal with serious cases. Honestly I don't need to be tested. I am at home 24h a day, I only go out to buy some food and that's it. I am very careful, don't touch nor talk to anybody and wash my hands the minute I come home. I am not saying I won't have it but I am reducing the possibility.
I might be wrong, I am not an expert, but the "real problem" with the Covid-19 is not the virus itself. The real issue is that it's very contagious and a lot of people need medical assistance at the same time. The information we have from medias is that "only" 1 to 2% are dying due to the virus and most were already facing other health problems. Thing is that it's easy to an hospital to deal with 10 infected people, not so easy when you have hundreds of them.
Yes the West missed an important window. This is why we are all in lockdown - it's simply impossible to test everyone
with symptoms quick enough and do the tracing quick enough to isolate those that need to be. Part of the problem is also that we're too stupid to follow instructions and stay home. We always think these things happen in movies or elsewhere.
Now, in case it's not clear nobody is talking about massive testing of everyone. Even South Korea didn't do that. But we still didn't ramp it up fast enough so now you isolate everyone to allow time to catch-up. Still doesn't mean people
with symptoms should not be tested. And you need to increase the criteria pool for testing as much as the testing capacity makes it possible. It's far from a waste of time. They absolutely need to know if and when the measures result in a plateau of new cases. Once the number of new cases is squashed (you only know this from testing), you can relax measures but at that point you have to start massive testing any time someone has symptoms, and do serious
tracing and isolation so infections don't spike again. The tracing and compliance is super important at that point. A single douchebag not complying can cause another spike.
You are correct that the problem is the infectiousness of the virus. But it's not that alone. Measles is 10X more infectious and just as dangerous. The issue is nobody has immunity (until they have caught it and won, symptoms or not) - there is therefore no "walls" to stop it from spreading. That "herd immunity" if you will (with Measles, the "wall" are created by all those that are vaccinated). The sheer numbers of people getting it at the same time is the issue as you point out. The hospitals being able to cope vs not is being estimated as 0.5-1% fatality vs. 5-7% if the system collapses. In the current situation without therapies.
As I mentioned above, the antibody test will be very important. This is what you use to see if someone has had covid and recovered. There are so many variations in the mild symptoms and many asymptomatics. You can start administering that to the general population starting with essential service people. Those with antibodies are safe (cannot get it, cannot spread it) and will be invaluable to society.
Also, all those you tested and found as positive which recovered are in that "safe" pool. So you already have that data if you massively tested.
Bottom line is that not ramping up testing and not implementing strong case tracing = isolation until October (according to experts) unless therapies are found. It's far from useless.
