Re: arXiv = Academic Wikipedia
"Neither of the two (large and we'll known) universities at which I studied allow that. Which ones do?"
Well, maybe Memphis Motor Diesel College where you went doesn't allow it, but I've not known any US University that does not allow the public to walk in off the street and use the library computers to read journals the University has subscriptions to. (You usually just have to show ID.) I have been a student, post-doc, staff researcher or faculty member at these US Universities:
UC Berkeley, Stanford, Harvard, Caltech and MIT
I have spent substantial time on these campuses collaborating/visiting with folks:
University of Colorado, Carnegie Mellon, Florida State, University of Texas Austin, University of Houston, Georgia Tech, US Davis, UCLA, Tufts, + many more
Every single one of them will allow the public to walk in off the street and use the library computers to read journals the University has subscriptions to.
When I was part of startups in Silicon Valley & Boston, it was standard procedure to exploit this. All you have to do is show ID when you walk in. (And bathe regularly.)