i got this from about 12 years life experience as a full time babysitter for numerous families. i honestly don't have any proof, beyond what i've seen. most kids will use whichever one feels right. most parents cannot help themselves and interfere with the process by trying to "teach" them the "right way" of doing things. you would have access to the scientific studies, but i don't know if its been explored. most toddlers will eventually settle into using one hand over the other for most things, thereby having a "dominate" hand. however i personally think people who aren't forced into one versus the other are better at doing things that require both hands to have dexterity. such as typing, or piano, etc.
but thats really a personal theory that may be full of holes.