More options in the Rendered dropdown menu

when we select "Rendered mode", the dropdown menu is always the same, regardless of what render engine is selected.

It would be nicer if it is context-sensitive, providing more options depending on the selected renderer. Maybe even an option to switch the renderer from it.

As an example, if we select the Workbench renderer, We would have more control over the rendering in this dropdown menu if we switch first to solid view, do the changes (ex: change light direction), then switch back to the Rendered view. I don't find this logical. In this case, the Rendered view dropdown menu should for example have the options that in the Solid View.