They've changed it now so it should now be possible to let most tests performed by a public health authority or an nhs lab be reported on the app.
This seems like the equivalent of saying that we can't have carbon monoxide alarms in this building because they keep going off.
In other words: if I was infected and attended a rave, a policeman interacted with me, and you interacted with that policeman two days later, you'd probably want to know about that fact and consider self-quarantining.
The comparison works if you add that the building is always filled with CO and that this is a known fact and that people in it are pros and take the appropriate measures. In such case, CO alarms are just noise.
Police evolve in a high risk environment and have procedure against that. Because of that and the security requirements of the Police, it has simply been concluded that the downsides of installing a third party tracker on a police phone outweighed the upsides.
However, it's just as likely that the app is spyware given that it doesn't, and can't link with any COVID tests you have via the NHS, only those done by Serco.