Promoted from a comment by Woody
The problem is that personhood grants corporations all the rights of being a person while giving them none of the responsibilities or penalties. People can be incarcerated or sentenced to death for crimes, corporations can’t. People eventually pass away, and are forced (by death) to pass on their power and/or belongings to others (and pay a tax on the transfer in some cases), while corporations live forever.
At best corporations should have a smaller, lesser sets of rights, tailored to meet the state of being they represent. That set of rights should take into account the fact that they’re effectively immortal, and can’t be punished via incarceration. If vampires were real, I’m sure we’d have a separate set of rights and penalties for the immortal undead than we do for living mortals. And when you think of it, how is a corporation any different than a vampire?