That's part of it, but not even the most important part. The other half is this: Can the US government announce that the New York Times may no longer run stor

That's part of it, but not even the most important part. The other half is this: Can the US government announce that the New York Times may no longer run stories critical of administration policy? Can they confiscate Apple's cash reserves to help pay off the national debt? Can they, without permission or a warrant, march into Google's data centers and read through all the email stored in Gmail? The answer to these questions is, respectively, no, no, and no. But why? The reason is not that the NYT, Apple, and Google are people with rights to free speech, property, and privacy; rather it is because the shareholders of these firms are real people with such rights, they do not lose these rights merely because they have organised their affairs to take the corporate form, and it would negatively impact their rights if the courts did not extend protection to the corporations they own. In other words, corporate personhood is a legal fiction which is deployed when (and only when) not doing so would impair the rights of real people. This explains why the NYT gets free speech rights (it would negatively impact the free speech rights of Sulzberger family who own the NYT to take them away), but doesn't get to vote (since not letting a company vote does not impact the rights of real people to vote). TL;DR: The main reason for corporate personhood is so that the government can't violate peoples free speech, property rights, privacy right, etc just because they have organised their affairs as a corporation.