You have to understand, once somebody drops off the GPS and goes underground they could literally be anywhere. If they fill the metro stations etc. with BT beacons, thats still not going to get it to the level of accuracy it needs to be.
I understand a fair bit... I worked for a nursecall manufacturer for a couple of years, a few years ago now... we spent a *lot* of time trying to work out how to add location to alarm events while keeping the users' pendants low power, in ways that didn't also leave room for massive invasions of privacy or allow for incorrect locations to be sent.
That was a very hard problem, and AFAIK the work on that project is still ongoing (as a background kind of thing) years after I left.
The thing is, you've stated the problem with infection risk yourself... looking at the infection cluster data we have so far, a person's infection risk is about a person's proximity to an infected person indoors for an extended time.... it's not actually about *where* you are, but *who* you are near for long periods of time.
BLE beacon tech on a smartphone can give us that. To some degree.
now hear me out.. Yes it's obvious and I understand that the beacon app going off RSSI can't tell if you're 1m away from someone with a stud wall between you, or 5m away in the same room... that's definitely a shortfall in what the technology offers... BUT you can still identify long term proximity events... what you do with that data - refining it into usable information - becomes a problem for the people doing the actual contact tracing..
In other words the dumb open source BLE app isn't "the contact tracing", it's an important tool in a sustained and serious contact tracing effort.
scenario one:
1) I, an un-diagnosed plague bearing wretch, go to a restaurant.
2) you go to the restaurant next door and get seated at a table right next to me, but on the other side of the wall
3) our phones make beacon friends as we sit down for an hour and eat our respective meals.
4) the next day I feel bad.
5) the day after i feel worse, and get tested
6) test comes back positive.
7) I give my app's recorded beacon buddies to the contact tracer people, and give them a list as best as possible of everywhere I spend extended periods of time over the last few days before I got sick (thanks, google location history!)

they find you in my list and contact you.
9) they confirm where you were on the day our beacon friendship blossomed.
10) they discover you weren't in the same space as me, and realise that you're probably not at risk.
Scenario 2 - the diff edition:
2) on this day cruel fate made you pick the same restaurant as me (I mean we're beacon buddies right, it's natural we would have the same tastes in pizza) and sit across the room, all socially distanced like we're not really beacon buddies. but we know different.
10) they discover we were in the same room for an hour. so you get tested. AT the point where it's highly unlikely you would be contagious or sick. so you need a test too.
11) you come back positive (I'm really sorry, buddy.... I.... I didn't know... I had no idea....)
12) you've just been given the chance to save everyone you spend time with from a big chance of being infected. Also you've got the chance of commencing any available treatment right at the onset of infection rather than once you're very sick.
TL;DR is:
beacon app bad
people using beacon app intelligently good.