Action potentials propagate by depolarization of one section of the membrane causing depolarization of an adjacent section.
It is necessary that this depolarization be greater than threshold. If the amplitude of the action potential were to drop below threshold, it would fail to propagate. Additionally, it would be quite slow and inefficient.
The tuber cinereum is the "swelling" at the ventral surface of the hypothalamus (Subarachnoid space surface) at the base of the infundibular stalk. The median eminence (a circumventricular organ) is an elevation on the ventricular surface of the infundibular recess of the 3rd ventricle.