Does it actually help the passengers?
Do you pay attention to the information if you have a connecting flight?
Yes.
When I hear the connecting gate info, I am looking at the terminal map. I know where we will arrive, then can calculate which way to turn when I exit the jetbridge. Right or left.
Then, I check the first TV monitor I see to confirm the gate, and continue to check TV monitors as I walk to the connecting gate.
I keep PDF files of the DFW and ORD American Airlines terminals on my Kindle, so I can quickly look it up if the gate announcement comes while I'm reading my Kindle.
Finally: I sometimes travel with my husband, who walks with a cane. If, while on the plane, I see it's a good distance between the arrival and departure gates, I just walk right out and flag a disabled persons electric cart without having to hesitate.