Actually, Elmo refers to himself in third person because that is a developmental stage most kids go through. The English system of personal pronouns is complex and it takes time and brain development to grasp all the rules (I, me, you, her/him, she/he, and a proper name can all refer to the same person at different times-- for someone just developing language skills that is a lot to make sense of and learn to use properly). Elmo reflects a very common stage in language accusition most (or at least many) children go through. It lets young kids (2-3 year olds) relate to Elmo and gives them confidence in their budding language skills.
I'll grant that Baby Bear's speech can be a little too precious at times, but I don't see anything wrong with it. Some kids have lisps. I don't think any of us would argue Sesame Street shouldn't show characters in wheelchairs for fear children will want to mimic the character and be in wheelchairs too. (Yes, I know that is sort of an extreme example, but Baby Bear suffers from a speech impediment that, in real life, would either correct iteself in time or require speech therapy.) I don't know what was behind the creation of Baby Bear, but Sesame has tackled so many other similar topics, it makes sense that they would have a character with a lisp.