Information shares all of the downsides of the public commons: because it is freely available, no one wants to pay for the maintenance costs. JSTOR charges fees for access to cover the ongoing maintenance costs associated with storing access to thousands of journals and millions of articles published over several centuries. Note also that JSTOR provides assistance with locating articles relevant to the user's needs (i.e., library functions), and such services are frequently more valuable than its archival functions.
A wiki will not suffice to maintain access to this information; Wikipedia and Wikileaks have shown that. You would end up with all of the articles but no practical way to find the particular article or articles you are looking for.