I never had a problem with this in TNG. After all, if person A wants to call person B over a comm channel, those two people obviously aren't standing in the same room. Therefore, by default, we cannot tell whether Riker hears the "Picard to Riker" bit instantaneously (which would be impossible, because the computer doesn't yet know the call has to be routed to Riker when Picard says "Picard to") or after a slight delay. We will just have to accept that there indeed is a slight delay there that is cut out for dramatical reasons when the camera cuts from Picard to Riker.The person on the receiving end hears the call at almost the same instant the sender spoke.
Yes, this isn't 24. We don't see both sides of the conversation in split screen. I imagine Picard taps their badge, says who he wants to talk to, then the computer establishes the communication and replays the "Picard to Riker" bit.
As for the "no response" thing, it's apparently not as if Worf waits for an actual person at the other end to say "Hello" or anything. After all, Worf doesn't hail anybody verbally himself, either - he merely pushes a button that sends out the automated hail.
So obviously it's more like Worf hits the "hail" button, and at once gets the rude automated "incoming messages blocked, especially yours" signal from the other end. No need to wait for two people to actually exchange superfluous words there.
I figured it was like establishing a connection with a server. The Enterprise tries to establish a connection on a well known frequency on the other ship. If that ship is listening for communications, then the Enterprise will get a near instant response. If they aren't interested then it will be immediately apparent.