The reality is that this practice of "cold calling" originated back in the days of analog radios, and in the days when there wasn't as much radio frequency traffic. I'd bet that section in the AIM hasn't changed in 40 years. I'm not saying it's a bad practice, as it certainly has applicability with certain facilities, but you can also apply some common sense to the equation as to when you need to use a "cold call."
For example, if you're flying out of a busy Class D airport, there is no reason you need to cold call Ground Control. They're going to be ready for you. If it's a slow day, you might need to reconsider that. When I was based in Lafayette (LAF), I cannot recall a single time -- even on the slowest of days -- when I ever needed to repeat my callsign or request to ground or tower. They had a 100% success rate without a cold call from the pilot.
At another facility like a Class C or B tower, where they need to enter your information into the computer, a cold call is appreciated. Not only do they need to look for you out the window, but they also need to prepare to enter a short string into the computer.
Flight service, on the other hand, needs a cold call every time. Their voice switching system is different than the one used by FAA ATC facilities, and they do not transmit on all frequencies they are working. That's why you sometimes experience a 2-3 minute delay when you call the Radio frequencies; those briefers are usually talking to another pilot.
That said, if you use a cold call like "Skyhawk 1234," you don't need to take any additional time explaining to the controller that you're a "Cessna Skyhawk 172" on the subsequent call. It's little things like that that tend to irritate controllers. Just be clear and concise about what you're requesting, cold call or not, and your efforts will be appreciated.