Consider also the scenario where A reports symptoms on day n. They have logged contacts with 10 people on day n-2, 10 people on day n-3, etc. With the NHSX des

Consider also the scenario where A reports symptoms on day n. They have logged contacts with 10 people on day n-2, 10 people on day n-3, etc. With the NHSX design, you might warn back to n-6 but might be able to determine that the riskiest cohorts are n-3 onwards. Since symptom onset distribution can be modeled, if by day n+3, not a single person in the n-6 and n-5 cohorts have developed symptoms (and maybe you've managed to get a -ve PCR from two n-5s - the fact that you have the contact graph means that you can use that data to adjust your risk score for all the others) you've now got a really good case for letting the n-5 and n-6 cohorts out. These models will be refined over time as well with new data. The presence of a central system which has some of this information lets you extrapolate from limited information. If you have infinite PCR tests and can logistically get them to potentially infected people very quickly, get them back to a lab, and get them tested then maybe this doesn't matter but not even South Korea's capabilities are infinite and there is no way the UK would be able to test all those people rapidly.