> Because corporations are just groups of people operating as one legal entity

A corporate entity has rights and powers that ordinary people do not, so they are more than "just groups of people". They are independent entities all their own.

Further, they can only exist because the government grants them that privilege, and the government can technically place any restrictions they like on them. In the past, the government used to require that the corporation serve the public good as part of the conditions for their existence.

I don't think it's right or accurate to characterize corporations as just "groups of people" and therefore they should have the rights of people. The law and the courts don't think so, either, which is why corporations are treated differently (with fewer rights) than people are.