Douglas's problem has not only already been solved, it's been solved without the assistance of a third party app, which I think is the most suitable solution to any OS X/macOS problem.
(If the widget can be deleted in toto, I don't see how a single component can be so critical as to not be deletable individually.)
We crossed in the mail, Douglas.
The new Great Equalizer is the SEND button.
In Memory of Harv: Those who can make you believe absurdities can make you commit atrocities. ~Voltaire