But suppose A starts showing symptoms, tests positive. We can immediately notify B1, B2 and B3 that they need to quarantine, immediately. Before they start showing symptoms. And therefore we're cutting down on the time that they were infectious and spreading. Therefore generation C is only a couple of people instead of dozens. We can notify C generation as well, immediately if we wish. This causes a large quarantine - there are a lot of false positives who are quarantining without being infected - but it would massively reduce the spread. If you can immediately test all of generation B and C, you can perhaps avoid some of the quarantining (assuming a negative is reliable).
Maybe contact tracing misses some, maybe some new infected come from other countries, maybe some people don't quarantine when told. All these things keep the infection going. But it can be held down to a manageable level.
The trick is to NOT stop testing once your case count starts going down, instead give the test to everybody that wants one.
A few million spent on 99.9% negative tests daily > a few billion spent on the economy being shut off daily
So I think the word manageable is doing a lot of work here. Specifically, manageable to the hospitals, which is what I believe most people mean when they say this, does not do anything to manage consumer confidence. Which my entire question is about. How do I, as an individual consumer, feel confident enough in the systems set up to go back to some semblance of normal? Learning that my chance of getting infected from going to the grocery store has dropped from 20%? to... 5%? 1%? Whatever the risk is, it needs to be multiplied by the average number of places a normal consumer went to over a week before this outbreak. Which means that I'm still gonna get it eventually, just I might not block somebody else from getting a hospital bed. Which is obviously better than nothing! But I really think people are missing the human aspect of precisely what this entails.
Consider user stories. As a single mother do you still feel confident going out to get groceries knowing there's an n% chance of getting it and bringing it home to your kids? If you die there's no one else to look after them.