Playing devil's advocate here:
Assuming like any other station, they have at least a reporter and staff on hand or on standby should something serious enough happen that warrants breaking in after midnight (or after 11pm, in WNYW's case).... Aren't you essentially getting the same newscast anyway? Why does have to be live just for the sake of being live? That's equivalent to sending the reporter to do alive shot outside of a courthouse that closed 6 hours earlier.
Finally, how is this any different from what all three broadcast network news divisions do? After all, viewers out west usually get a 3 hour old morning and evening newscast with little or no updates except for days when there's breaking news or a story affecting the west.
Again, just playing devil's advocate. I'm a fan of having it done live but if they feel they can save money and offer the same newscast, then why not?