The main arguments boils down to that since corporations are people and have free speech, and that a natural persons financial activity is considered protected speech, that a corporate person should have the same freedom as there should be no distinctions about the rights afforded to a person.
The entire argument would have been moot if we used distinct terminology
Perhaps the argument of Citizens United wouldn't have been made if we instead used the terms "Human Shmerg" and "Legal Shmerg", but exactly the same argument could apply to shmergness as to personhood when discussing the rights afforded to shmergs of one kind or another, and the conservatives in the US really want to deregulate everything.
The entire cry of "corporations aren't people!" is based and a complete misunderstanding of what a legal person is. You've done a great job at explaining.
Unfortunately, there are a lot of people who willfully propagate these misunderstandings. Because by saying "of course corporations aren't people, and everybody knows this except those dumb <other side>", it's an easy way to try to vilify the other side as dumb/evil. When the reality is that it's simply a tried-and-true necessary and useful legal concept, that virtually nobody but lawyers would even be familiar with in the first place, if it weren't for activists who thought it sounded scandalous.
> if it weren't for activists who thought it sounded scandalous
It wasn’t activists who first misunderstood the concept, it was the Supreme Court, who decided that corporate personhood gives corporations the same first amendment rights as real personhood. It’s not ridiculous to point out that if freedom of speech is implied by corporate personhood, it was insane to give corporations personhood in the first place.