Extremely important argument happening in DC at the moment.
Say a cabinet member walks into a university lecture hall and strikes a left-leaning professor with a baseball bat, claiming it to be a legal act. Litigation ensues, and the federal circuit court upholds the district court's holding that such things are illegal. Then, in a different part of the country, another member of the cabinet (and also a former television commentator) does the same. The question then becomes how to enforce the rule of law without these suits proceeding seriatum.
The present tactic is a tool of equity, the general injunction. Assume that goes away, due to historical abuse, under the principle that equitable remedies are not available where there is a remedy at law. If you have a government dedicated to lawfare, willing to survive any number of lawsuits as they continue to practice their unorthodox means of governance, how to maintain the rule of law?
First, the argument that constitutionally, under Article III, judgments can only bind the parties before them. This seems to contravene the equity powers granted the courts under the findings, and further, would prevent Congress from further modifying the jurisdiction of the appellate courts.
Second, the notion that a statutory class action could solve the problem. This seems an unwieldy tool, as it would require an institutional solution to every disputed claim; individual judgments would become hard to obtain, and thought useless.
Clearly, there has to be a solution in which, when a court says what the law is, it has some effect on the practices of the government. In the baseball-bat scenario, it would be good law in that first circuit that the government couldn't do that, and subsequent actions would awaken the usual tools -- constitutional tort claims against state actors, contempt sanctions, mandamus (the elephant in the room, perhaps), etc. Outside the circuit, a plaintiff might have to file suit, and arguably that's appropriate, in order to keep the boundaries of these percolating laboratories of democracy separate. If it's different than the first holding, then certiorari can resolve. If the same, then arguably a class action becomes a good tool if the government continues to maintain its practices outside of those circuits.
Alternately, filing suit at the seat of government could address the policymaking; jurisdiction over the cabinet member in their capacity in government should resolve the agency's practice. This is a more costly proposition in terms of the courts' power -- commanding the head of a cabinet agency to do something requires power, and costs influence.
Ultimately, making individual district judges the default backstop against flagrantly unconstitutional actions of the executive bats the bottom of your lineup card against the strongest forces of the adversary. Within the districts, the orders hold, and the power is proportionally balanced. Seeking a remedy in equity to bind the entire national government is a peculiar thing to have evolved in time, in that remedies in law are available, such as individual suits that write law for the states, circuits, or boroughs; suits against the agencies at the seat of government; or class actions defined by Congress. (Even where the relief is equitable in nature, the claim sounds in law, not equity, if you mentally piece the benches back together to consider the question.)
Top of the head, while listening to the argument in the middle of the mountains of Transylvania. Not advice, don't rely.