It's still very worthwhile to inform these people though. Some might be asymptomatic but contagious, some might be feeling ill but underestimating it might be COVID, etc...Honestly, if it’s taking a week just to get results in the U.S., then this sort of app won’t be very useful anyway. By the time somebody gets tested, gets their results, and the positive result gets into the system, anybody who had been in contact with the positive test patient will already have themselves potentially exposed hundreds of people.
Furthermore, even if the test takes a week, in the chain of contacts some people might have been exposed only very recently: the earlier they quarantine themselves or seek medical help, the better.