While the current driving force behind the desire to make corporations not the legal equivalent as a real person [is the concern over political contributions], there are other issues in play as well.
A person has a finite number of years of life to spend. So investing is based on a much shorter horizon. Companies can last for centuries and make investing decisions based on a completely different perspective.
As a result, fractions of a penny have more long term power for companies than for people.
Then we have the stilted political playing field where a company can massage the law to their advantage over time. A company isn't trying to feed a growing family, or save for a retirement. In contrast, people have other uses for the money they earn. Political campaign contributions are not high on the priority list of real people.
Another fiscal difference is the way debts are handled. If a company goes under, then the assets are sold and someone loses money. The people in charge of that failure are free to move on to another venture without any person fiscal repercussions. When a person goes under, they are hounded into bankruptcy and are thereafter victimized with usurious interest rates for decades.
Needless to say, I have some sympathy with the idea that when the "rights" of corporations (and other legal entities like labor unions, churches, veterans groups, etc.) are in conflict with those of real people, the real people should win. But I am not sure of the best way to solve the problem. One option is the "People's Rights Amendment":
Section 1. We the people who ordain and establish this Constitution intend the rights protected by this Constitution to be the rights of natural persons.
Section 2. People, person, or persons as used in this Constitution does not include corporations, limited liability companies or other corporate entities established by the laws of any state, the United States, or any foreign state, and such corporate entities are subject to such regulation as the people, through their elected state and federal representatives, deem reasonable and are otherwise consistent with the powers of Congress and the States under this Constitution.
Section 3. Nothing contained herein shall be construed to limit the people’s rights of freedom of speech, freedom of the press, free exercise of religion, and such other rights of the people, which rights are inalienable.
The Volokh Conspiracy suggests that this may not have all of the great benefits that its' supporters envision. I think they are right.
But that means that we still have a problem in need of a practical solution. One that places all legal entities in a secondary position when it comes to their "rights" relative to the rights of real, live, oxygen-breathing people.