Wordpress - Why use if function_exists?

Checking to see if built in WordPress functions exist before calling them is for backward compatibility which IMHO is not needed.

So if you see if ( function_exists( 'register_nav_menus' ) ) the theme author is supporting versions earlier than 3.0.

You still sometimes see if ( function_exists( 'dynamic_sidebar' ) ) Why? I couldn't tell you because dynamic_sidebar was introduced in 2.2.

Another reason to use it is to make your theme or plugin pluggable. A pluggable function is one that can be overridden in a child theme or another plugin.

This is done on the definition not the call and you use the ! operator to make sure it doesn't already exist before you define it.

if ( ! function_exists( 'my_awesome_function' ) ) {
/**
 * My Awesome function is awesome
 *
 * @param array $args
 * @return array
 */
function my_awesome_function( $args ) {
  //function stuff
  return array();
  }
}

When this is done a child theme or other plugin can override that function with there own.

The function_exists function is not an other way to load the function like add_action its for check your code to see that there are no other function with that same name so it will not break your code. From php.net:

Checks the list of defined functions, both built-in (internal) and user-defined, for function_name.

If you have the same function twice in your code it will break, thats why you prefix Your function with something else than wp_.

Read more: http://php.net/manual/en/function.function-exists.php