People want to match their behaviour with their attitude. Usually we think behaviour follows attitude, but if behaviour is constrained in some way, people tend to warp their attitude to fit the behaviour. That's one of the arguments for dress codes in the workplace, it puts you in the role, and also explains why you feel happier when you smile, etc.
Also, we sound subtly different when smiling, it's a bio-physical thing too, not just a manifestation of psychological state. I believe most people can actually detect if the person on the phone is smiling or not.
I would be really interested to see some research about it.
There are a bunch of hints, tips, or suggestions for using the telephone at work, but a lot of them seem to be "good ideas" rather than researched.
Other examples I've heard are "stand up if you want to sound confident" or "smile to sound happier".
It's a bit odd because there's lots of money and reputation going into telephone support, and a small edge would mean big savings.