As I understand it, the case for testing isn't all about death rates.
The two main advantages is that it allows planning with regard to lockdown measures, as you have more data about who is infected / where they are going etc.
It also helps with key workers, as people can get back to work more quickly once they have recovered / don't need to self isolate uneccesarily.
There are a few other advantages, such as the positive psychology of death rates being perceived as much lower etc.