The limited options (not just in selection but also on placement of features etc) are all probably very deliberate decisions. Disney (who remember nixed the idea of professional replicas of the Muppets unless they were poser replicas and not puppet replicas) were no doubt very specific about what could and could not be done so that one could create something "muppet-y" but couldn't end up looking like an existing character or close to one, even any "one-shot" whatnots that ever existed in any production.
I remember one of the coolest things about the toy Anything Muppet puppet that was released along with other toy puppets like Ernie, Bert, Cookie etc back in the early days of Sesame Street was that not only could one create all sorts of combinations, but you could essentially make a very close representation of Herbert Birdsfoot.