Many misunderstood the previous question, so I'll try to rephrase it.
Sometimes we see Riker's perspective: his badge blips and it says "Picard to Riker", and he answers "Riker here".
Sometimes we see Picard's perspective: he taps badge and says "Picard to Riker" and the immediate answer is "Riker here"
Until Picard has said "Riker", the system can't route the call. It would have to record "Picard to Riker" and replay it. Riker must start hearing "Picard to--" after Picard has finished saying "Riker". So, from Picard's perspective, there must be a delay, at least as long as it takes to replay "Picard to Riker", before Riker could possibly answer. Why isn't there a delay?
(Alright, so, everybody got that? Good! Out-of-universe answer: because nobody cares. Realistic Diction is Unrealistic, as TV Tropes puts it.)
Starfleet doesn't have a monopoly on communicators. Is this particular time-skip phenomenon ever shown on-screen, other than for Starfleet?