I use Linux, and my computer doesn't draw files (or anything else other than the default stipple) on the root window either; I have no desktop environment installed, because I do not use it and do not like it. (I don't use the Desktop, Downloads, Documents, etc directories, so I have deleted them. I can add directories with shorter names with whatever categorizations I need, and those aren't them.)
Files can be accessed by typing in their full path (with tab completion in some cases). (Some programs insist to use the GUI to select/list files rather than you can just type them in, and I hate this.) For searching files by name, ordering, etc, there is such commands as ls, and stuff that can be used.
For downloads, I will always type in what I want to save it as and in what directory, and usually I will use curl to download and redirect output to a file, or sometimes to another program is useful.
For screenshots, again I can use command-line programs; a program can make the screenshot, and then piped to the one that encodes it as PNG, and redirect its output to a file in order to save it to disk.
Command line interface is better, I think.