"Also, is this how we want our children to speak?"
This is exactly my issue with Elmo and the Teletubbies. Kids learn by imitation, and I can imagine the headaches some parents might come across if one of their kids gets into the habit of talking improperly. Other than that, the rest of Sesame Street besides Elmo was/is great for teaching kids quality stuff before they start elementary school.
My guess why Elmo does this is because it sounds "cute" to the writers.
Elmo speaks as a child does - hence, it's part of his personality and appeal to the little ones. Things we can relate to, we have a tendency to move towards.
Do we want our children to talk that way, of course not ... but it is a form of teaching as well. When Elmo says "Elmo is hungry", the child repeats "Elmo is hungry" ... hence, the child refers to Elmo in the correct tense.
Elmo mimics the behavior of many preschoolers. Like most three-and-a-half-year-olds, he doesn't always have the mature skills or knowledge to speak "proper" English. However, cast members and many of the other Muppets do demonstrate the proper usage of the English language.
that is probable purely an element. If he has been gazing Elmo then he probable picked it up from that Angelina Jolie's daughter, Shiloh, like's to be called John (from the movie Peter Pan).