Millions doesn't seem like an exaggeration:
1. The US, despite currently suffering the most, will probably not end up being the country with the most casualties. Once covid-19 takes hold in more densely populated poorer countries, there will be immense suffering.
2. 1918 flu cost up to 100 million lives, 1957 flu about a million lives, and 1968 flu about a million lives.
3. Total deaths worldwide is already >100k, and the known cases are still less than 0.03% of the population.
Would I give up my privacy to save a few thousand lives? Yes, but the scenario is incorrect. There isn't really a privacy sacrifice involved. I'm trying to think of the worst-case scenario in terms of privacy, but there just isn't one. Someone finds out that a device with ID 00:11:22:33:FF:EE spent 15 minutes with a device with ID 01:31:24:53:EF:AE. It's not worth so many people losing their lives for.