It's sometimes useful to use the same sidebar on many pages, so that you have a group of pages with a sidebar showing excerpts from similar pages. For this to work in the least painful way possible, it's helpful if you could have the same sidebar on all those pages, with multiple feature-a-page widgets showing each of the pages in the group.
It also means you would have a situation where the feature-a-page widget tries to feature the current page, which I imagine nobody would want to do.
Can the plugin be changed to auto-hide the feature-a-page widget when the featured page is the current page? You can do this with a simple change to fpw_widget.class.php in the widget(...) method. Just after you get $featured_page_id and find it's not null, you could do this:
global $post; // if we're featuring the current page, we're done if( $featured_page_id == $post->ID) return;