Why have circuits in the first place?
How courts are organized is mostly an issue of efficient and effective administration of justice, while balancing the ideals of justice itself (e.g. consistency, fair and equal treatment etc.). It is the reason why there is an intermediate level of courts in the first place and not every case is reviewed by the Supreme Court.
Surely it makes more sense to either abolish the circuits entirely, and have all decisions by higher courts binding on all lower courts regardless of state
Separate circuit courts on the same level means no circuit's decision is binding on another and a circuit court only needs to consider stare decisis for its own decisions, subject to binding precedents from the Supreme Court. A single court of appeal means that this court can overturn the previous decisions of itself.
Asking almost 200 judges to be consistent among themselves in the >44,000 cases they consider every year (out of which >26,000 are terminated on merits of the case) is a daunting if not impossible task.
And imagine this before the availability of instantaneous transmission and publication of decisions.
Of course, it is a hard job within circuits as well, and usually it is helped by the fact that lawyers on both sides intensively research on issues of importance. Eliminating the circuit would also increase the amount of research needed and slow down the court process even further.
The justice system must make a decision between the ideal of a uniform, consistent, predictable law, and the ideal of efficient justice administration. For example, the appeal rights from small claim courts are often limited. This is not because small claims courts make the correct decision every time, but filling up the court system with small value cases is detrimental to the administration of justice as a whole if other more important issues cannot be promptly resolved.
In the end, practically, you would either need to restrict the number of appeals considered (like the U.S. Supreme Court does), or divide the appeal courts into circuits. Different judges in the trial court already differ on their decisions, but important issues are hopefully uniform within the circuit, and then the most important of the issues are decided uniformly across the nation by the Supreme Court.
or, if you want to take a states' rights approach, limit the scope of these decisions to the state in which they were made.
This does not seem to solve any issues. Federal courts of appeal (mostly) interpret federal law and the Constitution where state boundaries do not matter, and their decisions are not binding upon state courts. Of course, like said above, a balance must be found between uniform federal law and efficiency and effectiveness of the justice system. But dividing into 50 circuits for each state does not necessarily improve the efficiency if the number of judges is not sufficient and contentious issues have to be argued and resolved repeatedly in 50 states.
This half-way house seems somewhat intolerable and I'm unable to discern any particular merit.
All this being said, I am not denying the problems and seeming bizarreness of circuit split. There are a lot of improvements that can be made to the U.S. justice system (or the justice system of any country).
Any large country (U.S., China, Brazil) or countries with concurrent jurisdictions (e.g. Canada and Switzerland) necessarily have different courts interpret the same law differently, although all systems try to resolve important contentious issues (e.g. through the grant of appeal to a higher court, or issuance of judicial interpretation orders).
It should also be noted that longstanding circuit splits (or similar phenomenon) are not the responsibility of the judicial system alone. For many questions, the Congress also has the power to make and clarify federal laws.