This logic is hugely flawed. Since we work off of a one-person-gets-one-ballot system, grouping people together (as in a corporation) and giving them a vote wouldn't make any sense. By contrast, you can't "use up" your speech rights: Each person is allowed an unlimited amount of legal speech, and I don't think there's a compelling philosophical argument that a group of people speaking together isn't protected. There may be _pragmatic_ arguments, but that's another ballgame altogether, since the entire point of the Constitution is that it's _not_ subject to the pragmatism/whims of the time.
I'm not saying that "corporations should be legally modeled as people" is an ironclad truth, but none of your objections make sense.