That's a logical fallacy. This app not being able to prevent all possible infections and having false positives / false negatives does not automatically mean that its sole purpose is to track users.
There are multiple scientific studies that support the use of an app as one of many measures for ending the lockdown which already takes away many basic rights at the moment. Even though viral RNA can be found on surfaces after hours this does not mean that surfaces are an important vector for transmission and all studies so far point in the opposite direction. What is very concerning however is that close to 50% of all tranmissions happen during the first few days of infection when the host is not experiencing any symptoms. In the absence of symptoms and given the many limitations of personal follow-up through the authorities (which gives them much more data on your person than this app ever could btw) an automatic notification system is the only way short of a complete shutdown to quarantine infected but currently asymptomatic patients and halt the spread of the virus.
Privacy-wise you would be worse of in any other situation as well. Do you want the shutdown to continue and police to be able to control you at any time when you leave your appartement? Do you want government workers asking the infected who they have been in contact with during the last weeks and them to give your name, address and contact details to the government? Do you want the economical crisis to continue and people to have to share all possible details with the government in order to get unemployment benefits?
Also, Apple and Google already control your operating system and have much more data on you than this app could provide them with through their OSs and all their apps. What they could gain would at most be the knowledge of wether you could have been in contact with an infected person. Leaving aside that their system as outlined atm would not even allow them to do that, what would they gain? For most people there won't be any lasting effects so there ara no charateristics inherent to the group that can be targeted. It will also affect a huge chunk of the world's population, chances are that most people will have to quarantine at some point and then that data will be almost worthless.