As a citizen of another country, I'm not aware of any country that is shipping tests to citizens at their homes. Maybe your numbers you quote are correct - there are other problems, like relying on people to report their positive test results and isolate. A lot of people would, but many also wouldn't, because they can't afford the loss of wages. You'd have to cover wages lost, or some percentage anyway, and that would mean requiring another test at a trusted facility, which increases the complexity again...
Maybe the concept would be workable, but it's also not a simple slam dunk, and again, I don't know that any country is doing anything like it.