I am having the same problem and can't seem to find a quick solution. I cannot use the delete key on my keyboard. I HAVE to go to the edit menu if I wish to delete tracks, artists, genres, or albums from playlists.
I used to be able to use the delete key, but now the edit menu does not have a shortcut listed next to the delete option.
I have also noticed this. Before, the delete key could be used to remove an artist or album from a playlist by selecting it from the browser window. This no longer works, and the menu item Edit >> Delete must be used. In addition, cmd-Delete would delete the artist or album from the playlist and library, with the option to move the tracks to the trash. This was an easy way to manage playlist content, and it is not clear why this function was removed. I would really like to get this back.