It’s not so much syllogistic form (as the Port Royal logicians discovered in the Middle Ages, Aristotelian syllogisms cannot prove that “If all horses are animals, then the head of a horse is the head of an animal.”) as it is being able to put things in symbolic form. Any elementary textbook on symbolic logic, which includes material on quantification, should suffice.
Then it’s not a logical fallacy per se, just a *non sequitur
*ETA, clarification: because the counter argument has nothing to do with the argument being countered, nor is it even denying its validity but rather abruptly changing the subject.
This, yes. Is there not a fallacy there? It would have to be an informal fallacy because there’s no way to quantify “shouldness”, but still fallacious.
Which is what I understand the definition of ignoratio elenchi to be (ignoratio elenchi being a subclass of non sequitur). Am I misunderstanding?
Well, what are you trying to accomplish by putting a tag on it? I mean, you could make up your own name if it’s that important. After all, the names of the fallacies weren’t given to us by God Almighty on stone tablets, they’re just the names that have been traditionally used in rhetoric textbooks of antiquity.
Which brings me to my point, classifications of fallacies are meant to help you identify weaknesses in your opponents’ arguments and devise rhetorically effective counterpoints to them. But just throwing out some Latin or Greek and sitting back smugly (“Ha ha. Ignoratio elenchi detected! Take that!”) is not rhetorically effective. So don’t focus on the trivia (“What would Cicero have called this?”) and instead focus on explaining why your opponent’s supposed refutation is actually no such thing.
(checks forum name)
I believe it’s possible to answer the General Question without making assumptions about, or evaluating the legitimacy of, the questioner’s intended use for the information.
However, it may ease your troubled mind to hear that I have no plan to do anything like what you describe. Why did I ask the question? First, I was curious. I have been noticing this particular argumentary phenomenon – fallacious or not – in several disparate areas of my experience, and, having noticed it, wondered if it has a name. If it has a name, especially but certainly not exclusively a Latin one, that would imply that other people have also noticed it, thought about it, and possibly written something interesting about it that I might enjoy reading. If Latin, that would imply some treatment of it in classical philosophy, meaning there’s probably a buttload of cool stuff to read out there on the topic, having been accumulating since European scholarship was primarily conducted in Latin, or even before. Second, in those discussions I do participate in, when I come up against this phenomenon, whether among my opponents or my teammates, it would be nice to have a handy nomenclature around which to organize my thoughts about why it’s not persuading me. I find terms and names for concepts generally useful for this. It also helps with the Googling.
You need a name for it if you want to research it.
No, actually you don’t. It is possible to commit the fallacy of missing the forest for the trees. If the OP is interested, I’d suggest a textbook on rhetoric, which is where these catalogues of fallacies come from. But you’re going to go on a wild goose chase, and end up retarding your research, if you think every bad argument has a precise name.
If, as the OP says in her most recent response, she wants to see what thinking has been thought on the topic, she’ll be much better served by reading Aristotle’s Rhetoric and similar works than by googling “ignoratio elenchi”.
Your unsolicited and off-topic advice is noted.
Ah, I believe that’s called “Argumentum ad Anglo-Saxum”. 
If there’s a technical name for the ‘fallacy’, that helps in researching it. If there isn’t a well-known technical name for it, then that’s useful information as well. All the OP is asking is whether there is a name for it or not, and for any useful further insights about this type of reasoning.
You seem to be well-versed with the literature on logical fallacies, for instance this Aristotle work you’ve been mentioning, which neither I nor the OP are particularly familiar with. So we’re asking you: is there a name for this type of reasoning? (It’s not ‘ignoratio elenchi’, that’s something different). Or if not, do you have any useful insights about this type of reasoning? Simply saying ‘not all fallacies have names; just go read Aristotle’ isn’t very helpful. Does this one have a name? Is it even a fallacy?
The predominant theme of the posts in this thread (by all responders, not just me) is that this counterargument is not really fallacious (that is, it can be a legitimate counterargument to say that more serious offenses have not warranted legislative intervention and that lack of intervention suggests that the proposed law is too overbearing) nor does it have a special name. There are, of course, rejoinders to this counterargument as well. That is the back-and-forth of debate. And that’s part of the reason why this counterargument doesn’t have a name. Sometimes, it is a good counterargument. Other times, it can be dispatched. It really depends on the facts of the matter. To think it can be surmounted just by uttering a name of a fallacy is elevating form over substance. The named fallacies, on the other hand, usually are just bad arguments. For instance, calling people names (or argumentum ad hominem if you want to be fancy and Latin about it) rarely signifies a well-considered proposition.
So, while I genuinely do appreciate the tactful way in which you formulated your response, the answer has not changed.