The apps that Google and Apple have been reportedly working on wouldn't really work unless it was turned on for everyone. It would have very large privacy concerns. However, if the one primary goal is to stop this virus, then it is a great tool. The phones keep track of who they are close to. When one person is diagnosed, the location history can determine what phones that person was in contact with and notify them. It would work even if the people don't know each other, such as standing side by side on the subway. That is a much better tool than asking the diagnosed person who he came in contact with in the last two weeks. He won't remember everyone, and he possibly won't even know who some of them are.
I said IF stopping the virus is the one primary goal. That isn't the one primary goal for many, even probably most people in the US. If that system was instituted involuntarily, some people would leave their cell phones at home. People who engage in suspect activities such as purchasing drugs or visiting prostitutes would probably leave their phones away from those locations even though they are probably at higher risk at those locations. It is a good idea in theory, but I have concerns how well it would work out in practice.