1) no, they can also use plugins.
2) you can't use widgets in a non-widget friendly theme
The benefit of widgetizing it is it lets someone who is afraid to edit files add something to a theme merely through the admin interface. If it's not a widget, they need to get in there, edit files, and potentially break it.
Also, if they switch themes, they won't need to edit the new theme files to use your plugin. So it can be a time saver even if they otherwise have the skills to add the function calls etc.
of course, not every plugin is appropriate as a widget.