Like in Photoshop, I'd like an option in Illustrator to duplicate the entire file, opening the duplicate in a new tab.
Tony Gray commented
right-click on tab and duplicate. that's what we want. Two clicks
Not sure if you'll see this or not... but, select all the artwork on your artboard, copy it. (Ctrl C). Create a new file, the size isn't important, you see why in a minute. Anyway, when the new file opens past what you have on your clipboard. (Ctrl V).
You should now see 2 artboards in this new file, 1 board has the artwork you just pasted, the other is empty. Select the artboard tool, select the empty artboard, and delete it. : ) You now have an exact duplicate of the original file.
I think this is what you wanted.