They should come up with some kind of removable metal cinch. I have a Cy Girl head (Aska) on a custom and the elastic always worried me (for the same reason as toylion--Star Wars figures with elastics melted to their hands).
On the other hand, I bought that head used, I've had it for five years (three in a smoking environment), and the elastic is only mildly yellowed. There's no deterioration at all.
It may be that the elastic reacts with paint, but not doll hair. If Baby Doll's hair is the same material as my cowgirl's, then it might not be a problem.