The 1/2 second delay isn't bad when you start thinking about everything going on between those two phones.
If they have the same service, the phone itself encodes your voice, sends it to the tower who sends it to a processing hub that sends the data to a distribution hub who sends it to the receiving tower processing hub and out to the tower(if they are on the same tower this still happens and most of the time has to be sent to another distribution hub) and then sends it to the phone where the audio is decoded.
If they are on a different carrier then the signal goes even further. With everything that happens behind the scenes, it's pretty incredible how fast you are able to hear the other person talk! And on top of all of that a single tower can be taking care of 20+ calls easily and the distribution centers handle thousands of calls at one time.
What you didn't include is that a digital signal is not transmitted when the sound is produced like on an analog phone- the phone has to listen to your voice, then digitize that packet of noise. So after you speak, before anything happens in your diagram, you've already lost 0.1 seconds or more within the phone that was never lost with analog. And the same is true when you are receiving, so what you hear is delayed by 0.1 seconds (or so) after the phone has released that chunk of data.
Now if you compound that by talking to another digital phone with the same packing & unpacking delays, you can shove your digital off a cliff...
You can't even call landline phones analog anymore. Unless you're calling someone across the street, its probably digitized. Especially if you dial long distance. All long distance calls are digitized fro transmission via fiber optic or satellite.