Ask HN: App idea for managing Covid transmission vectors

A thought I have just had, which the HN community is ideally placed to act on, on how to potential curtail the exponential growth of covid and other transmittable diseases:

If each person installed an app which logged Bluetooth IDs, along with a timestamp and perhaps signal strength, we could use this information to infer a degree of risk of transmission from one person to another: the longer a Bluetooth signal is nearby, the greater the chance of spread.

By logging this data, we can couple this with a means to have positive cases submit their BT ID, and immediately all those people who have been nearby can be notified, and can take precautionary measures.

I can see a number of challenges here, but in the current climate they may not be showstoppers. There is no need to post BT data to a central server, as it can be held locally and can simply monitor a centralised list of "hot" Bluetooth IDs.

What technical limitations have I overlooked? E.g. would this be at all possible on iOS, would this likely be too great a battery drain to the viable, etc?

Even though a tool like this would not reduce the initial rate of infection, I expect it to dramatically improve the identification of those at risk of having being infected, without requiring wholesale isolation of communities.

Thoughts?