It might not be impossible for Kennedy to continue to the end of his term, but being completely unable to speak is a severe detriment to being an active politician. Whatever charisma he might have would have to be transmitted through others - no more great speeches, no more impassioned addresses to the public, even in a case of disaster, some other person would have to speak on his behalf. International diplomacy, too, would be difficult and complicated for him. Even apart from the logistical challenges of this, I would guess that it would be intensely frustrating for Kennedy personally, to try to do all of these things while having to write down his thoughts or be interpreted for by someone else, and that alone might drive a decision to retire.