Your mother's argument is a brute-force one. Take lots more pictures, even with a low "hit" rate, and you'll get more hits. Having a feedback loop, on the other hand, is about improving your skill so you increase your hit rate so you're not picking 1/1,000 but 1/100 or better. With film photography I found that feedback loop so slow it was painful. With near immediate feedback in digital photography I can improve a skill by a small notch while standing there at the scene.

Immediate feedback also means I can correct a mistake. For example, if the focus or metering wasn't right, I see the problem right away and can correct it fast enough to capture the scene again. Back in the film days I'd only see a mistake days after it happened, and by then I was long gone from the scene I was trying to capture.