The proposed amendment would authorize Congress, states, and local governments to, for instance, (1) restrict what most newspapers publish, (2) restrict what most advocacy groups, such as the ACLU, the Sierra Club, and the NRA, say, (3) restrict what is said and done by most churches, and (4) seize the property of corporations without just compensation. (It might also allow restrictions on the speech of unions, depending on whether they are seen as "corporate entities.")
Nearly all major newspapers and magazines are owned by corporations; the same is true of book publishers, movie studios, record labels, and broadcasters. Indeed, if you want such entities to be able to raise money for their operations through the stock market, you have to have them be organized as corporations. Likewise, most nonprofit organizations are organized as corporations — that, too, makes sense, since it makes sense to have the ACLU run as a corporate entity rather than as a sole proprietorship owned by one person, or a partnership owned by a few people. Churches are likewise often organized as corporations, sometimes with a special sort of corporate status.