Lump, while a lot of con law types speculate all different ways about jurisdiction stripping, I’m not familiar with any special argument about “constitutional cases”, which you define as cases in which a citizen is suing a state or something, as being particularly relevant.
Quite literally–any case that isn’t brought to the Supreme Court under its original jurisdiction, is an appellate case, a case appealed up to the Supreme Court. The plain reading of the constitution is that such cases are under appellate jurisdiction, which Congress can restrict.
Original jurisdiction cases are rare, a couple a year, sometimes literally one or two. In such cases, note that the Supreme Court’s role is not to read appeals from the lawyers and listen to relatively brief oral arguments. They actually have to function as a full trial court. The Supreme Court is not super well set up to do this, and further, it’d take time away from the bulk of their work that they care about. So what they normally do in original jurisdiction cases is appoint a Master who basically acts a trial judge and conducts a more or less normal case. After his decision, the full Supreme Court reviews the trial judge’s decision, so in effect they get to work the case more like they do their normal appellate cases.
At the end of the day the real reason jurisdiction stripping isn’t super common is there’s a lot of built up respect for the institution of the Supreme Court as an equal member and equal branch of government. While this goes against your High School civics lessons, the constitution didn’t actually create three equal branches. The judicial branch is by far the weakest in the constitution itself, and also it is the weakest in more functional/practical terms. They can’t even collect a salary or get money for ink pens without Congress.
In most ways the legislative is by far the most powerful branch. But functionally the President’s veto power and his broad power to run the government, as the government itself grew, and as the dysfunction of the Congress has proved almost constant, has made the executive the most powerful branch in my opinion, de facto.
Unlike the other two though, almost the entirety of the judicial branch’s real power has built up entirely through custom and respect for it as an institution. For that reason there are things that don’t make sense if you imagine the founders writing up the three branches to be “perfectly equal”, that just wasn’t the intention. The real intention for the Supreme Court was it’d occasionally meet to hear a narrow range of important cases that the Founders thought ought be settled by some special high court.
Most of the day to day time of the early Supreme Court justice’s time was actually spent “riding a circuit”, they would literally be assigned to a region to conduct the business of lower level Federal circuit courts and do more “normal judge stuff.” I don’t think that jurisdiction stripping was seen as a way around judicial review, I think instead it’s that the founders imagined the Supreme Court having a much more limited role, and that specialist courts of various types would exist to be the last courts to hear certain appeals on various issues. Military courts, maritime courts etc, the thought was there’s no reason to even have stuff from those appealed all the way to the Supreme Court, why would it? But over time we’ve developed, through informal means and tacit acceptance, a system where we generally expect cases can ultimately at least be sent to the Supreme Court to decide if they want to take a look at it. The Supreme Court is also acknowledged as having a very valid role in deciding cases determining the constitutionality of legislation, and is expected to be solely the highest level appellate court, its justices are certainly not expected to “ride a circuit” any longer.
If the Congress just didn’t give a shit about any of this there’s all kinds of things they could do. They could just impeach the entire court. They could make the court have 30 justices and appoint 21 new yes men to do whatever the hell they want, they could reduce the pay of the justices to $1 a year. After that, the Congress could also basically just ignore Supreme Court rulings they disliked and if the President was like “okay” and kept executing the laws as before the Supreme Court has no recourse.
None of this happens because the independence, and current power, of our judicial branch is seen as deeply important to our functioning as a real democratic country, politicians that tried to assault it directly would fare poorly in the public’s eyes. FDR was a beloved President, but his scheme to pack the court was received very poorly, and in plain text it wasn’t even that egregious. His court packing plan basically allowed for the President to appoint an additional justice to the court for every current justice who was over 70.5 years of age, up to a total number of justices of 15. But his motivations were so clearly political, that it had very little support. The Senate committee chair responsible for the bill (a Democrat) was very much against it and never let it out of committee, and even Roosevelt’s own Vice President opposed the plan. Many other Democrats throughout Congress opposed it, all largely based on the fact they didn’t like FDR’s plan to politically maneuver the Supreme Court. On spec, it wasn’t remotely an unconstitutional proposal, but just the motivation of politically “out-maneuvering” the court was seen as very distasteful. This was in an era when most Democrats in Congress were pretty supportive of FDR, and the New Deal–there was one conservative justice in particular who was often the 5th vote in the cases that had struck down some New Deal programs, and he was largely the target of this action. So even though many in Congress wanted the New Deal legislation they were passing to be upheld, they weren’t willing to subvert the Supreme Court’s independence to do it.
Perhaps naively, I like to think Congress today would respond similarly to executive actions deleterious to the Supreme Court’s independence.