Schneier's a security expert, not an epidemiology expert. I don't think I'm going to put much weight in his opinion. The UK's epidemiology and behavioural teams have some confidence that this app will have an effect.
It doesn't need to be perfectly effective to be useful. Even a small reduction in R is very helpful.
For what it's worth, I was thinking of developing an app on similar principles a couple of months ago and I talked to at one of the Sage people. They were enthusiastic about it. There have also been papers modelling the effect.
I don't like Cummings' politics but he is a smart guy. I think he'd follow the science.
We took a deeper look in an article linked in another comment on this thread.
One thing that's interesting to think about more deeply is how difficult it is to estimate proximity based on the combinatorial explosion of different hardware, individual device peculiarities, battery levels and environmental factors (walls, glass windows, partitions, ventilation).
The very limited data published appears like interesting preliminary field work which finds significant variability in signal strength across hardware, and rather than concluding proximity estimations are useful, ends in a plea for OEMs to release factory calibration data for their BLE implementations:
