Pulling the plug out for 10 seconds
A lot of modern technology contains capacitors! These are like energy buckets, little batteries that fill up when you put a current through them, and discharge otherwise. 10 seconds is the time it takes most capacitors to discharge enough for the electronics they're powering to stop working. That's why when you turn your PC off at the wall, things like an LED on your motherboard take a few seconds to disappear. You probably could wait a different time, but 10 seconds is the shortest time you can be sure everything's discharged.
In my experience 0 seconds work just as well as 10 for restarting the equipment.
The reason in my opinion for the 10 seconds is only to ensure that the client has totally pulled the plug out of the socket. Some people just don't pull it out all the way unless they have to wait for X seconds with it in their hands.
I think there are 2 topics going on here within this question:
The value of waiting a period of time after removing the power from an electronic device. YES, 30+ seconds is a good "average" time to allow Capacitors, hard drives, RAM memory, etc have the time to power down and be ready for the 'power on' reboot sequence.
The proper way to 'power down' an electronic device. Best 'rule of thumb' is if the equipment has an 'on and off' button or switch USE IT. It's there for a reason. As anyone with the knowledge of how a PC operates knows there are important 'startup' and 'shutdown' sequences the equipment goes thru. Allow the equipment time to power down and power up properly. These sequences are necessary for successful operation. Otherwise stress to hardware, stranded files, bloated 'page files', voltage surges, etc... can cause more problems, on top of the one you are trying to fix.
Phoshi said well, but there could be another reason for that, a very less technical one: it is kind of related to social engineering.
The majority of customer care call center hires just...everyone! And there you could find someone that understand what you're asking, as well as someone who don't understand/don't care about, and the usual solution for every problem is (in the latter case) something like "Reboot" or "unplug and replug"! :D
Sadly, I saw that with my own eyes...
It's simple: capacitors last... And in some case more than 10 seconds. You must have heard from the cold boot attack, where they rely on just that feature of capacitors.