I pay attention because I like to hear where everyone else is connecting.
Personally, I don't put much weight in the connecting gate information. I'm going to check the monitors when I get off the airplane for up to date information. The information the flight attendant has is out of date by the time it is read out.
For novice flyers, I would think it is very re-assuring. I just hope it doesn't give them a false sense of security thinking they can go straight to the reported gate without checking the monitors.