I've never seen examples listed under a law, but it'd make them a lot less ambiguous and easier to understand.
For example, the 4th amendment (a law I'm familiar with) could've given a few examples of reasonable and unreasonable searches and seizures. The 2nd amendment could've given a few examples of "well regulated" and "the people". I think regular state/federal laws are the same.
Note: this isn't specifically about the U.S. constitution, but state/federal laws in general.
They are called “judgements”
Every case decided by a court is an example, in common law jurisdictions at least. When those cases are decided by an superior court they become precedents - binding “examples” on courts in their hierarchy and persuasive “examples” on other courts.
When you go to a lawyer for advice, she doesn’t just parrot back the statute, she looks at the precedents and decides whether the case decided by the House of Lords in 1848 or the High Court of Australia in 1912 more closely matches your situation.
Also, statute law often has examples written into them
Statues exist in hierarchies, Constitution, Acts, Regulations, Departmental Policies etc. and the lower you go the more specific the law is and the more likely it is to have examples. For example, this answer I wrote for another question quotes examples from the new-south-wales Evidence Act.
The problem with examples is that they shift our attention from the words that comprise the law, to the actual examples used. For example, the term "press" as used in the First Amendment used to refer to a particular means of dissemination text and images, which literally pressed ink onto sheets of paper. Technology has expanded in such a way that there only moving parts are your fingers and the keyboard. "Arms" used to be just muskets and flintlocks, but now there are many other kinds of arms. What Amazon does now has not imaginable under the 18th century characterization of "commerce".
Exemplification works at cross-purposes with generality: the more exemplification you give, the more likely it is that the word means A and not B. Had they constructed a list of examples of "cruel" punishments when the Constitution was written, that would likely have meant that the Star Trek "agonizer" would be a non-cruel punishment, and many things now prohibited as "cruel" would not be prohibited. Whether or not that is a good thing or a bad thing is a separate political question. On practical grounds, what examples clarify what is a "cruel" punishment?
The reason to not include examples as part of the law is that it would just confuse the question of how the courts are to interpret the law. It would encourage what some consider a questionable interpretive practice of trying to guess what the original lawmakers were thinking when they passed a certain law; it shifts attention from "what the law actually says" to "what you think the lawmakers had in mind when they passed (amended) this law". Nevertheless, laws are passed with lists encoded in the law, especially law that seek to enumerate the various kinds of "weapons": usually they contain a disclaimer "including but not limited to".
OTOH, educational material that non-authoritatively tries to explain what the law says is not a bad idea. Check out this website.
Laws can and do include examples - for example, searching for the incantation "including but not limited to" in legislation draws up thousands of cases where laws have included examples of some things or activities.
Some random cases:
As used in this chapter, “aquaculture” means the culture and husbandry of aquatic organisms, including, but not limited to, fish, shellfish, mollusks, crustaceans, kelp, and algae. Aquaculture shall not mean the culture and husbandry of commercially utilized inland crops, including, but not limited to, rice, watercress, and bean sprouts.
or
For purposes of this article, “abuse of office or position” means either of the following: (a) An abuse of public authority, including, but not limited to, waste, fraud, and violation of the law under color of authority. (b) A crime against public justice, including, but not limited to, a crime described in Title 5 (commencing with Section 67), Title 6 (commencing with Section 85), or Title 7 (commencing with Section 92) of Part 1 of the Penal Code.
Also, the Constitition of United States Amendment 14 there's an example of what is considered public debt:
4: The validity of the public debt of the United States, authorized by law, including debts incurred for payment of pensions and bounties for services in suppressing insurrection or rebellion, shall not be questioned.
It's up to the legislators whether they want to include examples or not. In general, examples do not change the meaning of the text, so for the purposes of brevity and clarity they are often omitted or removed unless the legislators want to emphasise a particular scenario or ensure that a potentially questionable element gets explicitly included - as in the case of public debts in the 14th amendment. Also, including a limited number of narrow examples may nudge citizens and courts to interpret situations substantially different from the provided examples as not applicable, so if the legislators intend that all cases fitting the criteria should be included with a wide interpretation, then they may intentionally avoid giving examples.
When you refer to "laws" here, you mistakenly assumed that all "laws" are statutes (laws adopted through the legislature / political process). Statutes are adopted and/or changed over time and the necessity of legislative history has changed with society. There are many statutes that are never changed simply because they are not controversial. There are many "code books" which contain the type of information requested here.
In any common law country (essentially any country which speaks English, including the US), the bulk of the law is judge-made law and/or interpretations of statutes in the context of actual cases or controversies. These are generally known as legal precedents and they have the power of law.
The entire purpose of legal research -- fundamental to any legal brief -- is to find either a statute or, better yet, a recent legal precedent applying the statute in the context of a similar or identical situation. Brief-writing is generally taught in law schools as a mandatory course; brief-writing is a very high-end skill that many attorneys never master; this is why appeals law is itself a legal specialty.
The main components of any common law jurisdiction's law library are books of the statutes which are commonly annotated (i.e. the statutory language is following by citations to relevant case precedents) and volumes of case precedents, generally organized by date and findable by the volume number, the series name of the relevant courts, and the starting page number. These materials can be contained in thousands of volumes, with significant differences among jurisdictions; all of these materials are now well organized and online.
The contents of statutes and cases are always in the public domain, free and online; most of the attorney-level materials are produced by private publishers who may add editorial content that is very helpful to an attorney.
For example in California, where I have practiced for over 40 years, a minimum physical law library would include probably about 1500 volumes, although nobody I know would subscribe to physical books today. Everybody uses commercial online services. Statutes have, for many decades, a legislative history which is prepared by legislative staff, are generally included in annotated books of statutes. I bought my own set about 30 years ago, at great expense, but today I consider those books pretty backdrop (clients are very impressed) but useless.
Please keep in mind that the practices and laws of each jurisdiction may differ; indeed, their differences are direct manifestations of the sovereignty of that jurisdiction.
For example, the 4th amendment (a law I'm familiar with) could've given a few examples of reasonable and unreasonable searches and seizures. The 2nd amendment could've given a few examples of "well regulated" and "the people". I think regular state/federal laws are the same.
Ironically, your examples show why examples are a bad idea.
The Fourth Amendment was written before 1800. At that time, believe it or not, the general understanding was that governments could not seize something from its rightful owner just because it was evidence of a crime. So the examples of searches and seizures would never have included searches and seizures for evidence!
The Second Amendment comes from the same time period. At that time, all major world powers employed privateers to operate weapons of war. Private individuals are not a realistic check on government power now as they were then and the implications for invading armies are very different. The examples would flow from premises that are false and it's unclear how you apply such an example.
First Amendment examples would not include anything remotely like Twitter, heck the telephone was more than 70 years away. They would have included the presumption that news is spread the way it was spread hundreds of years ago.
What do you do when the law is "X because Y" but Y is false? How do you make sense of that kind of mess.
Some laws do contain examples, but they tend to be laws that are very detailed and specific and that are frequently maintained. It makes a lot more sense to list standards and requirements rather than trying to state which things meet those standards and requirements in a changing world.
