A nit but corporations are groups of people with all the rights and responsibilities of those individuals. We only treat them as "a person" as legal shorthand.
Not quite. The whole point of a incorporated / limited liability company and equivalent entities (Inc, llc, Ltd, SA, GmbH, NV, etc) is that owners are only liable up to their investment, i.e. you are not responsible for the debts of the corporation; not individually and not as a group. You can lose your investment, but that's the limit of your liability. If the group of owners of e.g. a coal plant would have the "rights and responsibilities" of the entity, they would be collectively responsible for its debts, e.g. cleanup costst, if it goes bankrupt. As a corporation, the plant goes bankrupt, the owners lose their investments (their shares are worthless), but remaining debts and liabilities cannot be collected.
Because this creates moral hazard and can cause society to be left with unpaid liabilities (tax, legal liabilities such as cleanup costs) historically they could only be created by special government fiat ("royal charter"), an implicit collective acceptance that the benefits outweigh the risk to society, and their number was quite limited for a long time, with famous corporations like the Dutch and British East India Companies among the earliest examples. Now, however, anybody and their uncle can start a llc/corporation, and while in theory the managers can be held responsible if they act in bad faith (e.g. take out loans, funnel the money to Caymans, declare bankruptcy) this is not prosecuted nearly often enough.