COVID app?

[Frazzled13]

I’m genuinely not trying to be goady, and I’m not a conspiracy theorist but I just don’t get the point of the app for a lot of people?
I wfh, I don’t get public transport - the only people I’m within 2m of for 15 mins are DH and DD, plus my parents if we see them. They’d tell me if they had symptoms or tested positive.
I guess I’m just wondering what the benefit of it is? Would it alert me if I walked past someone in the supermarket who then tested positive? I wouldn’t be within 2m of them for 15 mins though so would that count?
I’ll download it if it helps, but my phone doesn’t have much space and the battery is shit so I don’t want to download it if I can’t actually see the benefit.
Am I missing something obvious?

People can be in a queue for a fish and chip shop or similar substantially longer than 15 minutes (think about 48 minutes is my record for that), unexpected public transport journeys, people in the house. Also allows for a much easier system of contract tracing following an outbreak in a venue using the QR code system.