Proposal for a way to reduce coronavirus infections by optimizing whom to test

One way to reduce the number of Coronavirus infections is to detect as early as possible infected people, so they can be quarantined earlier. In the ~5 days incubation period an infected person will unknowingly infect others.

So whom to test, besides symptomatic people? Test everybody who came in contact with the people already tested as positive (this is doable now, while the number of infections is still relatively small). But, besides family members and work colleagues, we don't know who are those people. Could be the cashier in a supermarket or gas station, travelers who shared the same bus, the Uber/Lyft driver... and that's how the infections continue to grow . We simply don't know all the people who came in contact 1-5 days ago with a person who just tested positive today. But there's a way to find out.

Everybody has a smartphone nowadays. If everybody's location would be tracked, each individual could be alerted if they were close to a recently positive tested person. So, we would know whom to test next. Those persons would be found & tested as well in next 1-8 hours, and quarantined if positive. They would stop unknowingly infecting other people, including family, friends and colleagues.

Technically, this is doable starting now, if people would agree on a privacy-respecting institution. It could be an open source app made by World Health Organization (WHO), which already collaborates with world-wide authorities. The data would be available only to WHO. They would share only what's needed with appropriate authorities and affected individuals. The app could also provide official alerts and science-backed advice.

There are some technical issues (eg GPS doesn't work indoors; server resources required to record continuous data from a few billion people), but we don't need to have a perfect solution. Major tech companies are good at solving these type of problems. They could also donate temporary cloud resources to WHO and prompt all their users to install the app.

There are some privacy issues, but easily solved (eg delete data older than 30 days). I'm ok to share all my location, name and phone number with WHO, but there will always be naysayers.

If this easy solution helps reduce infections even by 20%, could we simply agree world-wide on this one specific issue, and start as soon as the app is available? And how could this proposal be improved?