What you call an "unwritten constitution" is the fundamental idea behind common law, which is basically the default in majority-English-speaking countries. Outside the Anglosphere[0] the standard is "civil law", which means that the law is only the stuff that was actually written down and decided upon by the parliamentary body. Everything else is optional; you aren't forced to "obey precedent", but may "follow jurisprudence" if such rulings provide relevant argumentation to the facts of the case.
This isn't a left/right thing, it's a British/French thing. And being a former British colony, America is very strictly a common law country. That's why we even have to care about the Supreme Court at all. The Constitution merely says that there is a thing called a "Supreme Court", and that Congress can make more courts if it wants to. In the early days of America, SCOTUS got handed to them a constitutional crisis, squinted at the Constitution, remembered how common law precedent actually works, and said, "well, that means we have the power of judicial review".
So naturally, the Constitution always has an unwritten component; to get rid of that would be effectively making a new Constitution. What people are squabbling over is what should and shouldn't be in the unwritten component, not whether or not it exists. Originalism and textualism deny the unwritten component, but nobody is actually an Originalist or textualist. There's no historical justification for the people who wrote the Constitution to want a civil law interpretation of it. Remember, they were all British lawyers and politicians. What Originalists and textualists are actually doing is using their ideology as an excuse to overturn precedent they don't like. If they were really Originalists, they'd be shutting SCOTUS down.
[0] Sharia Law and Mao-style "We won't tell you what the law is" bullshit notwithstanding
My abortion example may have muddied my point more than it helped, sorry about that. Let me try to articulate it more clearly. I'm (mostly) not discussing common law as I am focusing on the federal level. Common law tends to be more of a state concept (except Louisiana). As the Supreme Court held in Erie:
"Except in matters governed by the Federal Constitution or by Acts of Congress, the law to be applied in any case is the law of the State. And whether the law of the State shall be declared by its Legislature in a statute or by its highest court in a decision is not a matter of federal concern. There is no federal general common law. Congress has no power to declare substantive rules of common law applicable in a State, whether they be local in their nature or "general," be they commercial law or a part of the law of torts. And no clause in the Constitution purports to confer such a power upon the federal courts."
There are matters of common law at the federal level, but they're not central to my broader point. When I say "unwritten constitution" I am referring to a set of laws, statutes, customs, and judicial decisions which together form an unwritten constitution that are non-binding to future legislative efforts. The Magna Carta and the 1689 English Bill of Rights still make up a part of the unwritten constitution of the UK, although the former is mostly symbolic at this point. However, no parliament can bind a future parliament in the UK. So if they wanted to repeal the 1689 Bill of Rights they could do so legislatively right now. The major advancement of the founding generation was the idea of a written constitution, one that could bind future legislators - and technically the other branches - so that the constitution itself had to be changed through a separate process. In other words Congress cannot repeal our Bill of Rights right now, it would have to go through the arduous amendment process. So when I speak of an unwritten constitution I am referring specifically to the non-binding nature of the laws and statutes that make up a set of foundational rules for a society. The phrases "unwritten constitution" and "written constitution" are fairly old and unfortunately are a bit of a misnomer in what they actually mean.
> The Constitution merely says that there is a thing called a "Supreme Court", and that Congress can make more courts if it wants to.
That's actually a good place to start for an example. Chief Justice Roberts stated recently that "[f]or more than two centuries, it has been established that impeachment is not an appropriate response to disagreement concerning a judicial decision. The normal appellate review process exists for that purpose." This highlights my point fairly well. The written constitution, the one that cannot be changed through normal legislative means, makes no such determination as to what is or is not appropriate and merely grants Congress the power of impeachment without even defining what high crimes or misdemeanors means. What I would argue has become a part of our unwritten constitution is as Roberts describes, a set of appellate courts with specific jurisdiction where the appropriate course of action for an unfavorable opinion is to appeal. However, Congress can add or remove inferior courts and determine their procedural rules and jurisdiction pretty much at will. In other words this set of courts, laws and customs developed by the legislator does not bar a future legislator from changing it to something wholly different if they so desire.
Another example would be independent agencies under the executive which has become a hot button topic lately. Article 2 Section 1 states that "[t]he executive Power shall be vested in a President of the United States of America." However, for a long time now we have had independent agencies which were created legislatively with a certain degree of insulation from Presidential control. I would argue that this is another example of a part of an unwritten constitution that does not bind any future legislator. It's also an area of extreme friction between the written one and the set of laws, customs, and precedent that we have developed over many decades.
Hopefully those two examples are more informative as neither are really central to common law.
> In the early days of America, SCOTUS got handed to them a constitutional crisis, squinted at the Constitution, remembered how common law precedent actually works, and said, "well, that means we have the power of judicial review".
That deserves a reply far longer than I can provide here. In general while I see the utility of judicial review I would argue it doesn't make sense when it comes to disputes between the federal government and a state, i.e. the federal government via the judiciary gets to have the final word over what is constitutional when a state challenges the federal government over the constitutionality of some federal action. I would also argue that Marbury v. Madison was one of the first bricks of an unwritten constitution being constructed as for the most part everyone just passively accepted it, but it is not explicitly called out in Article 3. However, there are good arguments against this.
This isn't a left/right thing, it's a British/French thing. And being a former British colony, America is very strictly a common law country. That's why we even have to care about the Supreme Court at all. The Constitution merely says that there is a thing called a "Supreme Court", and that Congress can make more courts if it wants to. In the early days of America, SCOTUS got handed to them a constitutional crisis, squinted at the Constitution, remembered how common law precedent actually works, and said, "well, that means we have the power of judicial review".
So naturally, the Constitution always has an unwritten component; to get rid of that would be effectively making a new Constitution. What people are squabbling over is what should and shouldn't be in the unwritten component, not whether or not it exists. Originalism and textualism deny the unwritten component, but nobody is actually an Originalist or textualist. There's no historical justification for the people who wrote the Constitution to want a civil law interpretation of it. Remember, they were all British lawyers and politicians. What Originalists and textualists are actually doing is using their ideology as an excuse to overturn precedent they don't like. If they were really Originalists, they'd be shutting SCOTUS down.
[0] Sharia Law and Mao-style "We won't tell you what the law is" bullshit notwithstanding