Journal pay walls: why why oh why?

I think this is a common complaint. But maybe I'm missing something, and someone can fill me in, either on a workaround or a reason behind the problem.

When you're looking for an article in a journal or a conference, like, say, "Measuring Alertness" by Michael I. Posner, you can't freely get the full pdf. You often run into sites like this. If you belong to a university, they often have a subscription to the journal, and you can log in and get your article. If the author was kind enough to post the file elsewhere on the internet, you can find it via Google scholar or something, and then download it directly. Otherwise, you're left with three choices: pay something absurd like $20 for a pdf, subscribe to the journal (in this case, the ever-thrilling "Annals of the New York Academy of Sciences) for an even more outrageous fee, or do without.

I believe, and tell me if I'm wrong, that no human in the history of the earth has ever chosen choices 1 or 2. So the net result is that top-level academic research is limited to those lucky few who have access to a university.

But sending a pdf costs nothing, and because nobody pays, journals aren't making money off of these walls anyway. Journal owners could easily enable all 6 billion of us (or at least the 2 billion who have internet access) to do any kind of research, anytime, anywhere. Wouldn't that be at least a bit of a net positive to the world?

Counterpoint: if they didn't have paywalls, universities wouldn't pay for huge memberships, and journals would go out of business.
Counter-counterpoint: well this is fine too. (what are journals for? so peer-review can happen? why not just let this self-organize?)