Actually, the Sesame Street characters each have a specific age. I think Elmo is 3 1/2. Big Bird is six, though he started out younger. I believe Carroll Spinney talks about this in the A&E Sesame Street biography. I don't remember all the ages, but I think a lot of them are mentioned in Sesame Street Unpaved.
The idea is that each character represents a unique stage of early childhood development, providing every member of the Sesame audience with a character they can identify with, and providing Sesame Street with characters going through all the same developmental stuff as their audience.
That's why Elmo isn't very good with personal pronouns-- kids his age don't generally get that. It's why Big Bird and Snuffy tend to play more complex imaginative games than Zoe and Elmo-- older kids can create more elaborate imaginary worlds and act them out, younger kids tend to act out what they have seen and experienced (Zoe, being younger, would probably be unlikely to make up a game show with all the rules and whatnot that go into that, she can, however, be a contestant on Bird and Snuffy's game show because she has seen game shows on tv). Like wise, Bird and Snuffy are not likely to pretend a coat is a playmate because they know coats are inanimate objects (they'd use Radar or something else that represents a live being) while Zoe isn't tied to those sorts of ideas yet and for her it is perfectly plausible that a coat or a rock could talk and play with her.
Probably more information than you wanted. As a sociologist, I find the detail and thought behind each of the Sesame Street characters fascinating. I don't know of any other kids show that has ever gone to such lengths to be accurate and realistic about child development and it is one of the things that makes the show so great and effective as an educational tool.
As for the Sesame merchandise-- yes, there is an awful lot of Sesame baby stuff. But there is also some regular Sesame stuff. There is a line of cars (just a little bit larger than matchbox cars) with Sesame characters driving that are nicely made and not babified. (I'm particularly fond of the Count in his purple convertible.) There are some other, small, mostly plastic toys that are more accurate representations of the characters, but nothing that really leaps out at me. I don't really understand this-- some Sesame babys are fine, but Elmo is only 3 1/2 and Zoe is a bit younger, what's the point of turning them into babies? (rhetorical question there, of course I understand what's going on, just seems silly to me)