The reason they can do this is they acted quickly and they have mass testing and contact tracing of the people who test positive. We can't keep the entire world locked down for months on end. At some point, we have to start opening things back up and the only way to keep the viral coefficient below 1 is if we can quickly and efficiently identify & isolate everyone who has potentially been exposed to the virus.
Today, only a tiny percentage of the people in your city have corona virus. In the US, we have around 100k official cases out of 330M people (0.03%). Obviously that number is way under-reported, but it gives us a rough idea of how far along we are on the exponential curve. For now, we're still searching for a needle in a haystack. First, you need mass testing, including people without symptoms. Otherwise it will keep spreading from person to person unknowingly. Second, you need to figure out who else they have possibly infected and isolate them too.
For the first time in history, most humans on this planet are already carrying a tracking device with them at all times. We just need to figure out how to utilize this data while still respecting users privacy and making sure we don't unwittingly usher in a new-era of government and corporate surveilence. The crazy thing is Google, Apple, Facebook, the NSA, and all of the phone carriers already have this data collected on just about everyone. But they don't want to freak us out by revealing just how much data they have on all of us.
Of course, many places will need extensive lockdowns to reach that point.
I think you are right about this and furthermore, non-optional bluetooth tracking is just going to encourage people to leave their phone at home when they go out, especially if they are on the fence about whether or not they are a danger. If they need something they are going to go get it.
We need a rapid cultural adjustment that causes people to voluntarily minimize spreading.