I don't even remember if we got Santa gifts as a child. As a parent, we give gifts from ourselves (opened on Christmas Eve) and gifts from Santa (left under the tree to be discovered on Christmas). I can't imagine any reason to have all of the gifts come from Santa. Why would you want your children to think you didn't give them a gift? I know someone whose child did ask her, sadly, "Why did I get a gift from Grandma and Uncle Joe and Aunt Jane, but not from you and Daddy?"
Another word of warning... beware of letting Santa be the one who always brings the extravagant, hard-to-find gift. That sets up expectations that Santa can get anything. If Santa always brings typical gifts, and the big gifts come from Mom and Dad, it's easier to explain that you did not get a Wii because Mom and Dad couldn't find one. You don't want Junior to say "That's okay, Santa will bring it!"