This is one of the ways, in my opinion, that Joomla and Drupal are friendlier to themers. Most template tweaking will involve dealing with one file -- index.php (Joomla) or template.php (Drupal).
In the case of Joomla, this gives Wordpress slightly more flexibility, in the sense that it's easier to change out the layout of a page, based on what page is being served (slightly easier to have a different layout for the home page, about page, contact, etc.) if that's what you want. Either Joomla or Drupal will allow you to use separate files as well -- just not quite as neatly.
Drupal has an advantage over BOTH Joomla and Wordpress ... in the sense that you can use the "Context" module. What the context module does is allow you to manually specify, through the admin GUI, what "areas" of your site are to be active, and to manually manipulate the layout of the various elements, depending on what page the user is on (and various other factors). Rather than sifting through 20 different template files to figure out which one has your header code for a given page. And if you ever dive in to panels, that will give you a GUI interface to alter the layout of everything, without ever having to touch a template file.
The only downside is that, some people might find the process of sifting through 20 different template files ... less difficult than having to navigate through Drupal's admin interface. And that's only a mild exaggeration.