The real question, which you touch on, is what do you want to talk to your neighbors about? Crime data is certainly one thing, but local email lists that I'm a part of indicate others:
* can I borrow a tool? * anyone have a recommendation for a service (lawnmower, roof replacer, etc, etc)? * I have free stuff in front of my house. * I have friends who want to move into this neighborhood, anyone looking to sell?
I think that event organization is possible, given enough uptake.
Disclaimer, I used to work for a real estate brokerage that was pursuing a neighborhood model (8z.com) and was a competitor of NextDoor.