So, I have the same suggestion. I’ve had my system for less than a week, but so far, this is probably my biggest annoyance. I understand that a few things would delay it – from what I’ve read, when you use motion zones, it records for 4 seconds before deciding whether to stop and trash the recording – so with that feature enabled, 4-5 seconds is probably the soonest one could reasonably hope to get a notification.
Ideally, that would also include a live view, but even if it doesn’t, it would be useful to know the motion is happening. Sometimes it’s quicker to peek out the window than pull up the app anyway, for example.