The walled garden of academia is not so fruitful as outsiders are led to think it is.
We struggle year after year to pay salaries and still have money to buy the equipment and material we need for the projects, we don't have that much left to spend on buying access articles that we and our peers wrote and that we and our peers reviewed, all for free while some publisher makes millions on it.
To be fair, I haven't set a foot in my university for 3 years (planning to return soon!) but since I still send them the occasional email asking to be registered for a course I'm considered active there and get access to a lot of publications as long as I'm logged in to their systems.
Do any universities offer something like "passive studentship"? i.e. you pay only a small fraction of the tuition, it does not include any courses, but you may attend the facilities and specifically the library and get access to the university network. If that existed, hobby researchers and the like could get access to all these journals for a probably smaller amount of money.
The state university library here has a [membership program][0] that gives you access to the library and its various subscriptions -- so effectively library donors get access. Individual membership is under $50/year, so it's definitely an affordable option. Not sure if it gives remote access to their network (they used to have a web proxy server for off campus students, don't know if they still do); you may have to go to the library and use the computers there.
Many universities actually do have a program to give townfolk library cards, including journal access.
That said, the best way to get a research paper in CS is to check the author or lab's website and, if it's not there, e-mail the first author directly.
My other comment covers this. There is actually an upside to spatio-temporal control, which is that anyone who walks into a university library can access the licensed material for that library. Of course in this day and age such physical restrictions on access seem absurd.