Could you give us a short list of apps that can delete a file from within the program? I don't think I have any, myself. Most apps just use the OS' navigation dialog for finding ( Opening ) and Saving files. I've never seen a program that had a "Delete File" menu item. I've always just trashed the ones I didn't think I needed anymore, sometimes also storing them on other media before doing that...
Email programs are slightly different. Some ( Eudora, Mail? ) keep messages as separate files and you can delete individual files/messages without harm. M$ keeps messages in a database that you are not allowed to touch.
Don't confuse the "Delete" item in the "Edit" menu for what you want to happen. The Edit menu usually only operates on what you may have selected in a particular window; it would delete the part of a file that you have selected ( highlighted ). Many programs don't have a "Delete" item, they simply use "Cut".