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but we would lose herd immunity for the flu

Nobody does contact tracing for flu, let alone common cold (which is caused by a bunch of different viruses)

Also, common cold mortality is extremely low.

We could, though, It's not practical today, but it's definitely something that humanity could achieve, especially with technology like this.

Even if it's not the most important thing we could do, eliminating influenza and the common cold would be pretty fricking awesome.

He's saying that because this technology will exist, the possibility will exist. Plus this will no doubt not be the last emerging virus.

To answer your Q, Op: yes. Provided Apple/Google doesn't remove the functionality in a later software update.

Could the cons be as incredible as the pros?