The best I can come up with is because it is straight up magic in nature. A worgen bite effectively forces the magic from the Scythe of Elune into you and makes you channel Goldrinn magic.
Once you get your mind purified, you are no longer unconsciously forcing Goldrinn magic into people and thus, would not be passed on unless you do so purposefully.
This is of course just head canon, and really has nothing to do with Tess not being suitable for leading Gilneas, since she is literally the only person in the line remaining to do so.