Touché on second point, but who forgets their phone these days, really? I haven’t forgotten mine ever that I can remember.
Another reason: "lets meet at a corona party, no cell phones permitted".
Basically, we have to stop 2/3 of infections to get an R<1. If 2/3 of the population use the app honestly and we keep up some other measures (no indoor events where people are in close contact, wearing masks while shopping, no visitors in nursing homes and hospitals, etc.) then this might be enough to contain the virus until we have a vaccine.