WPF: Programmatically click the default button

A one liner:

System.Windows.Input.AccessKeyManager.ProcessKey(null, "\x000D", false); 

Background

A WPF Button with IsDefault set true registers itself with the AccessKeyManager, specifying the carriage return char (0x000d) as access key.

So AccessKeyManager.ProcessKey() will invoke the default button's ButtonBase.OnAccessKey(), which raises Click event and executes any associated command.
No need to loop controls to find the current default button.