That's the issue addressed in The Price of Ignorance: The Constitutional Cost of Fees for Access to Electronic Public Court Records by Stephen Schultze. Here's the abstract:
The United States federal judiciary maintains a system called PACER, “Public Access to Court Electronic Records.” PACER is the public gateway into the electronic repository for documents filed in federal court. In lieu of appropriating funds for operating the system, Congress permitted the judiciary to collect fees. Through the web, for a per-page fee, members of the public may access documents that have traditionally been part of the free public record. The fees have persisted for decades, despite the fact that Congress intended for the judiciary to move away from user fees to a “structure in which this information is freely available to the greatest extent possible.”
This paper argues that the federal judiciary has erected a fee structure that makes public records practically inaccessible for many members of the public and for essential democratic purposes. The per-page fee model inhibits constitutionally protected activities without promoting equally transcendent ends. Through this fee system, the judiciary collects fees at ever-increasing rates and uses much of the revenue for entirely other purposes — in an era in which the actual cost of storing and transmitting digital records asymptotically approaches zero. PACER should be free.
This paper examines the public’s interest in free electronic access to federal court records, and consider the relative strength of legal and policy arguments to the contrary. Section I performs an accounting of the true costs of a free-access regime. Sub-section I.A. examines the monetary cost of providing electronic access. Sub-section I.B. considers the privacy costs to individuals who are identified in electronic court proceedings when digital records erase some of the “practical obscurity” that prevailed in a print-only era. Section II details the benefits of free electronic access to federal court records. Sub-section II.A. describes how this access benefits the public’s understanding of the law, whereas Sub-Section II.B outlines how free access enhances the transparency and legitimacy of the courts. Section III argues that, in the tradition of Richmond Newspapers v. Virginia, free access electronic to court records is a constitutionally necessary element of the structure of our modern judiciary.