[csiegert]

The sarcastic answer: You have to pirate papers. There is a popular Russian hub for science papers that contains almost every paper ever published in the last couple of years. It is used by many academics.

Almost no organization can afford to pay for all the stores, so even universities have limited access in the sense that they can only offer their students and staff a limited selection of what is available. Subscription fees are too high, single journals are often only available in bundles with other journals/topics, increasing the price further. Publishers act as gatekeepers to (often publicly funded!) knowledge.