It is NOT designed to track locations. It is only designed to signal you IF you have come in contact with someone with the virus. It is limited in its functionality. It sends you a message that you have been exposed and probably offer options as re action to take. That is it.
Now , if you have an inherent distrust of technology, the government..........then that is another story.
If it does not have your location data, how does it know you have been in contact with someone? The only way this would be useful is if it WAS storing your location data in real time. It would then compare your locations with the covid carrier and send you the alert. It's fine to be ok with it doing that but don't pretend its not doing it.
In addition to my distrust of the government to not to use the data in ways not intended and/or not leave it exposed to hackers who could do God knows what with it, I think it will drain my battery and my data. For this to work, it will need to be monitoring my location and relaying it constantly. Location services are a drain on my battery and data is not unlimited or free.
All these and more are the reasons this app will not be on my phone.