It's not the time it takes to place the call, though that's generally better, it's the lack of need to make conversation. A conversation consists of:
Person A: Person B?
Person B: Go for Person B.
Person A: What room is on fire again?
Person B: Room 568b.
Person A: 10-4.

VS:
Dammit, I can't remember what room was on fire. I guess I'll call Person B and find out.
Person A: Calls, waits for answer.
Person B: Hello?
Person A: Hi Person A.
Person B: Hi Person B. What can I help you with?
Person A: Well, I'm down here on the second floor, and I was wondering what room you had said was on fire, I'm ready to go there now.
Person B: Hold on, let me look that up.
Person A: Ok.
Person B: It looks like it's 568b.
Person A: 568b. Ok, I'm heading there now.
Person B: Thanks, give me a heads up when you're done.

Now, you'll say that's not fair, you're saying more in the telephone call. But none of it is important.

Now, it doesn't look like the PTT scenario is much faster. But look at person B. Person B had his hip buzz, when he came to a stopping point in his current sentence, said yes, and got a question, gave an answer, and when directly back to whatever he was doing. Also, everyone in person A and person B's vicinity can know which room is on fire if they want to listen. This in infuriating if you're in a movie theater, but when you're all on the same team, it lets everyone keep track of what's happening a little better. If person B leaves the conversation he was having face to face, that person knows and understands exactly why without needing to be told.

Another point in their favor is that phone books are managed centrally somehow. Which means, I show up on site and am issued a walkie with everyone who's anybody's name in it. I've just eliminated ten to twenty "here's my cell number, what's yours" conversations. When you're only at a site for a week, this is a great time savings.

I fully understand that you'll never appreciate the convenience until you've experienced it first hand. But it really does work better in specific situations.