A right click to export from the project browser would be ideal, especially if Revit could be clever enough to offer only the most commonly used export options for the item you are exporting.
Multiple selection exporting would be even more useful!
i.e.
If you export a render it automatically offers the image export dialog
If you export a Plan or Elevation it offers the CAD formats dialog
personally I would use it for renders most often, the "copy to clipboard" option does not allow you to change the resolution etc. to do this currently you have to render the view, save to project, drop down the "R" click on Export, scroll down to "Images and Animations" hover over this and wait for the pop up then click on the "Images" option (and if you are in a hurry and miss it is back to clicking on "R" again
)
If the above is a too much to ask for even allowing you to customize the export box so you could have the commonly used ones at the top would be fantastic! (may post this as a separate idea)