And then think about it some. The premise of Mr Schneier's article presupposes that the application is a total replacement for human contact tracing and provides a diagnosis to the user. When you set up a strawman it is easily knocked over, and that he proceeded to do.
These apps, if well designed and used, can provide an additional source of potential contacts for the intelligent human beings doing contact tracing. The contact tracers will certainly will get application-reported contacts that do not result in transmissions, just like the majority of contacts elicited via interview will not have resulted in transmission. The contact tracer will not get application-reported contacts were contact existed unless both parties are running the app: just like the gaps they get from interviews with positive cases, and the things they cannot know like indirect transmission. Application contact records can also be used to prioritise interviews (a 4 hour contact is more likely to be problematic than a 10 minute one). If the use of the app detects one extra case that would otherwise have been walking the street passing on the love then it has more than, "absolutely no value." Even if the application data identifies a new positive case faster than it would otherwise been detected then it has more than, "absolutely no value."
That's not to say there are no privacy concerns, and there are certainly better and worse ways to craft an application.
In Australia the tracing app (notice the singular) does not autonomously announce to users that they have been in contact because, to quote Men in Black, "A person is smart. People are dumb, panicky dangerous animals and you know it." The app has been used only a few tens of times to allow human contact tracers to interview potential contacts of confirmed positive cases (https://www.abc.net.au/news/science/2020-06-11/coronavirus-contact-tracing-app-covid-safe-no-close-contacts/12343138). It has not yet, to my knowledge, taken an infectious individual off the street that would not have otherwise been detected, but that may simply be because in Australia we have been blessed with very low COVID numbers in general and almost no community transmission. (https://www.abc.net.au/news/2020-03-17/coronavirus-cases-data-reveals-how-covid-19-spreads-in-australia/12060704?nw=0)