It would be nice, but I think it could cause problems. One issue is that it wouldn't work well to switch to student view on an assignment, quiz, or discussion that wasn't published or that had dates set to not yet be available. If that happened, it would either kick you out of the course or show you that your activity was published and ready, when in fact it isn't. I would bet that is why you need to start on the home page or settings page as those pages are unique. That way you can then navigate through your course to ensure it's published and ready to go.
A quick workaround. Copy the URL of the assignment, quiz, or discussion you want to view as a student. Then go to the home page, switch to student view, and then paste the URL in the web browser.
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