To easily find out which applications are installed on your system there should be a category "Installed Applications" on the list located on the left side of the window. So you can easily remove applications without searching them. This would be especially great for new users who can't use yum, etc.
I think it's not a big problem to implement such a feature and it would make managing packages much easier and faster - even Microsoft Windows has a list of installed applications.
There is a menu item to filter for "installed applications" :)