The implication is that it is always legitimate for the child brand to establish its own identity. However, this is not always the case. There is at least one instance when a baby brand should stay close to the fold of a parent brand: When the unity of the parent brand is at stake. That is, if the baby brand’s having its own identity will threaten the parent brand’s unity, there is a problem.
One solution to this dilemma is to fold the baby brand back into the parent brand (renaming it, at least partially). The benefit is to flow brand equity from the baby brand back into the parent brand. The risk is that brand equity will flow out of the baby brand, but not flow into the parent brand – with the result that there are two flattened brands.
If it is not possible or desirable to fold the baby brand back into the parent brand, the parent brand should indeed let the baby brand go and surround it with “siblings”—related subbrands that can establish a kind of “melting pot” family for the parent brand. E.g., Coca-Cola has not only its namesake cola brand, but also Minute Maid juice, Powerade, Nestea (with Nestle), Fruitopia, and Dasani (source: http://en.wikipedia.org/wiki/The_Coca-Cola_Company). All of these subbrands have their own identities, but all of them are also known to be related to each other as part of the Coca-Cola family.
In general, although there are baby brands that supersede their parents and deserve to have their own spotlight, it is not desirable for a master brand to have a proliferation of subbrands—unless each subbrand contributes something concrete and valuable to the master brand portfolio. If the master brand does not exert control over its baby brands, it will be overrun with divisions and offices each wanting to brand their own activities, each leaching equity from the master brand probably before being ready to exist on its own.
So it is a careful balance that has to be struck between parent brand and baby brand—proceed with caution.
Part 1 of Parent brand vs. baby brand is here: http://blumenthalonbranding.blogspot.com/2007/08/parent-brand-and-baby-brand.html