I noticed that the feature to clear the shell window has been a
discussion topic in the IDLE-dev archives for a few years. Here's an
extension that can clear the contents of the shell window. It provides
"Clear Shell Window" under "Options" and a <Ctrl-L> key binding.

The source code provides two methods to do this. The
ModifiedUndoDelegator prevents changing the contents of the text widget
before "iomark". One solution is to disable the filter, make the
changes, then re-enable it. Another solution is move "iomark" to the
beginning of the document. Any thoughts?