That's why we have the privacy issues we have today, all the monitoring, surveillance, etc didn't just come out of nowhere. An emergency happens where people just want action to come, then action comes through legislation, government grows and they don't give back that control after the crisis.
It's useful to separate two discrete issues.
A) What math and encryption will and will not do.
B) What power structures (include here not just government, but all those commercial interests that want your cloud data) was.
My point is that it is 100% possible and practical for the tracking necessary to trace person to person transmission of Covid-19 at level A, without (B).
It's important for the Crypto community to stand up and say things like this, because otherwise the exact trap you cite will be fronted and no one will say it's not necessary to give up privacy.