The modern habit of pronouncing the number zero as the letter ‘O’ should be banned from public broadcast.
I've never given this much thought... I use both interchangeably unless I'm talking to an airline rep. I know from experience that mixing up zeros and "O"s can keep you from finding your flight info.
I can see how someone not used to the custom, or someone whose primary language isn't english, could get confused - particularly in a stressful moment like trying to get emergency help. I didn't know that Australia uses 9-0-0 for emergency services.
I don't think you're going to have much luck changing something that's so ingrained in people's normal usage/conversation. What seems like a "what's the big deal" to most of us can be life threatening to someone else.