You are somewhat mischaraterising the phone apps. They are certainly not perfect, but nor are they useless. As provided in countries that use them, most, if not all, don’t track location. So there is no need to keep data on movements. Processing power is close to zero. Phones simply handshake with one another and exchange a key recording the exchange. That can be used after the fact to allow alerts to be sent to phones that made the exchange. Is is essentially a secure and opaque way of automatically exchanging phone numbers.
Distance is potentially a problem. The phones can’t tell if you are on the other side of a wall. They use Bluetooth which is inherently a short range protocol. In principle they probably could measure distance quite accurately over Bluetooth, but the power needs probably go up. The problem will be false positives, which so long as they are not too large in number won’t be an issue.
But using phone apps does really only work when the infected populace is well under control. It helps significantly in stamping out flare ups. If you are only getting a few people a day, or less, tuning up positive - you can find the contacts fast. Clearly there is a point when so many people are still becoming infected that everybody’s phone will be bleeping every day telling them they need to be tested, and it is useless. That isn’t a problem with flare ups, that community should still be in lockdown.
Phone apps don’t replace contact tracing, but they should make it a whole lot easier, efficient and effective.
Here in Oz, although we have the app, and we probably have enough downloads to start making it effective, the news so far is that it has only been used once to trace contacts for one person. Then again, where I live, we have had only one person - who flew in from the UK and was already in isolation - test positive in the last month. For us the phone app makes a great deal of sense. We can open up, and if someone comes down with the virus, even if they were clubbing furiously the week before, we could find most people at risk and get them tested. It potentially allows a much greater loosening of restrictions. But only after things have been brought under control. Not before.