Ah, but the corporation DOES sue people. You wouldn't say "A variety of people in an organization that produces fast food known as McDonalds sued a variety of people in an organization that produces shoes called Nike", you would say "Mcdonalds sued Nike".
Strictly because the latter's shorter than the former and linguistic convention has accepted that speaking in the latter manner is acceptable. The former is actually accurate. The latter is, and only is, a way to avoid having to spell it out quite so explicitly. That doesn't magically make McDonalds or Nike things that exist outside a person's head. It is directly equivalent to me saying "epistemology" instead of "the study of knowledge." Specialized language and not a wit more.
Like I said, to a heavy degree that's basically the crux of it. We've stated that a collective -- which is only a thing in a cognitive sense, and doesn't actually exist beyond that -- is an individual, and somehow deserves some of the rights (but not all of the responsibilities!) of an individual. If a corp, or a union, or whatever, exhibited the same degree of independence that a human does to, say, its lungs, I might be able to get behind the concept of groups as individuals.
But, they don't. Corps are fully controlled by individuals, and explicitly demonstrate the leading and control of individuals. The only times this seems (and only seems) to blur is when we allow those controlling individuals to hide behind the collective mantle of whatever it is they're directing... and allowing that perception -- and
exponentially worse, attempting to enshrine it into law -- is causing extremely blatant problems.
I'd put it bluntly. The courts screwed the pooch with this one, and a reading of the constitution that does what you're speaking of is one that
seriously needs to be reexamined. Calling things that are blatantly not people, people, isn't something we should be doing. Establishing laws for the recognition and protection of collective action? Yes, we need that. Calling collective action anything but what it is? No. We don't need that.