I think an OS-managed popup window is superior to a page-managed modal since it allows you to move the window out of the way or even switch away from it, where as a page-managed modal is generally fixed in place, blanks out the parent page, and the only way to get back that parent page would be to dismiss the modal which discards your input.

I'm also not sure whether the accessibility concerns are substantiated - surely window management would be a well-trodden path for any screen-reader user and whatever you build yourself in-browser would have different and unexpected semantics that would require the user to get used to it.