> Android would be "impaired" if it shipped a general-purpose mail client rather than one designed specifically for Gmail?

Android includes (or at least used to include) a generic email app called Email.

> It would be "impaired" if part of the setup process was to select an app store[0], a browser[1], and a maps app[1]?

You can have all of those, and more, with custom ROMs like Cyanogenmod, or even with AOSP alone.