Your proposal has a drawback: it would make it very easy to work with several pages at once (as you would store the page outside the session by default), which does not work as the driver can only have 1 active page at a time (which is why a session has a single DocumentElement instance).
Thus, ``visit`` is not the only way to move to a different page (a form submission or clicking on a link will most of the time navigate to a different page)