Its funny because you wouldn't NOT nickname your creatures in other games. I'm really under the impression that people don't nickname their 'mon because they're too used to calling them by their species name or because names like "Charmander" and "Squirtle" are different enough from Salamander and Turtle that it feels like they already have names.
I mean, if a game gave you a dragon and said "What will you name this dragon?"... Would you call it "Dragon"?