Why does umount automatically remove the mount point of a drive that has been mounted with a file manager?

It is not up to umount to delete a directory so from command line you need to do it yourself.

You can use a script for that:

#!/bin/bash
mount_point=/media/directory
umount $mount_point && rmdir $mount_point &

and save it as umount.sh.

The mount_point might be better off as a variable so you could so

./umount.sh /media/dir

Something like this

#!/bin/bash
mount_point=$1
umount $mount_point && rmdir $mount_point &

So why is it automatically removed when I run umount on a drive that has been mounted with a GUI file manager?

The answer to this is more likely a design decision. I have not found any documentation on this (maybe someone else can provide a link ;) )