Propagate a Shortcut Across All Modes

Just wondering if there is a way to propagate a shortcut across all modes?

For instance; if I set “Rotate” to the “E” Key in object mode, then I would want rotate to be E in every other mode that applies, like UV, Pose etc. as well.

Set the hotkey in 3D View -> 3D View (Global) section.

That does not work, but it would be more intuitive if it did.

Edit, it works but I didn’t realize it because the redundant shortcuts need to be manually removed. Thanks Stan!