Is there a way to prevent apps from staying in Dock after quitting? Certain OSX apps seem to have a tendency to stick around in the Dock, even though there's no user-facing setting to prevent this behavior. Is there a defaults command that prevents apps from enabling "Keep in Dock?" 

I know about defaults write com.apple.dock persistent-apps -array (intentionally empty), but this has to be run manually, and repeatedly. Any ideas?
I think I understand your problem.. Open System Preferences, Click on dock, uncheck "Show recent applications in dock". This should probably solve your problem.