Creating subsite from template doesn't keep theme/header - why not?

In SharePoint Designer 2010, I opened a subsite and then did "Save as Template". I then created a new subsite from the template. The new subsite creates fine, but it doesn't inherit the theme from the templated subsite, nor does it have the header (site logo, navigation, etc). I was expecting an exact clone of the original site (with or without content depending on whether I select the "Include Content" option when creating the template). Is that not how a template functions in SharePoint?