Amazon is not the only one catering to people with kids, Google is working on something similar for Chrome. Granted, the feature has more use cases, enterprises being the prime example.
Chrome will support managed user accounts, similar to a regular user account on operating systems. These accounts will have limited privileges.
One user acts as the root account and gets to select what the managed user can do and see. Even the sites available for browsing can be limited as well as apps.
In fact, Google hints at app/content packs in the Web Store, which will dictate what managed users can access.
There are several more features that would come in handy, the Google SafeSearch can be enabled, presumably without the possibility of disabling it.
Signing into Chrome can also be disabled as well as Private Browsing and the ability to delete history. Parents who want full control over what their kids do will love these features.
They'll also come in especially handy on Chrome OS. The feature is not enabled yet, but you can check it out by running a recent version of Chrome, from the dev channel or Canary builds, and using the --enable-managed-users and ---managed flags.