My belief is that contact tracing is a cultural non-starter here. There are people who protest with large, semi-automatic rifles because they don't want to wear masks inside private businesses.
There's absolutely no way they're going to trust a contact-tracing process championed by the government, even if there's no way for the government to access the data.
I suspect much of the population will continue to ignore the virus and winter weather will cause a spike that will cripple hospitals.