If you really want to do that, you could create a launch daemon (basically a plist used by the OS). There are several GUI-based apps that make that a very simple task. My favorite one is
LaunchControl.app.
This site has over a dozen other alternatives.
It may be a bit more difficult since WC needs to 'see' the Quit command twice. However, the Manual suggests a very simple AppleScript that can handle that for you and that the launch daemon can initiate.
I'm not sure why you would want to limit this operation to just WC. You already have the ability to schedule a complete Shut Down and Start up process with the Energy Saver System Prefs. Using that process would eliminate 'problems' from not only WC but any and all other apps (as well as System tasks) that may be creating memory leaks, etc.
I think the majority of WC users operate the app on computers running 24/7. Many of us use dedicated, older Macs and only Quit WC when the OS requires an update. I think the better solution is to determine the 'illness' rather than 'treating the symptoms'.