If someone is informed of a potential or likely infection, but then typically [chooses to/is able to] go about their day the same as usual, then what's the point of tracing them?

Initial modelling that showed contact tracing to potentially work assumed: 80% uptake, over 70s to be isolated in any case, and people to strictly follow isolation rules, none of which was considered politically possible in the West: https://www.bbc.com/news/technology-52294896