Its purpose is to make it more likely for me to hear the doorbell when we are out of earshot of the real thing, e.g. when we're in the sun lounge with the doors closed, or when we're in the garden. It's an electronic bell with two receivers, the second of which is interfaced to the BB, which then notifies me via Pushover on my mobile phone. Most of the notifications arrive within 2 seconds, although there was one yesterday that took 20 minutes - which is of course completely useless for the purpose. Like I say, it's a minority. But then I also get notified when I'm out; equally useless, but who cares?
I don't understand why you think it might be annoying. If someone rings the doorbell and I'm at home, I want to know - that's the point of a doorbell, after all. And if someone leaves a package at the door and buggers off, I'd rather bring it in before it gets rained on.
David