Fair use is seen as one of the more difficult laws to define in logical consistent terms, so lets start there. Can we create fair use definition in such way that a mathematical function separate all that should be defined as fair use, and all that should not based on unbiased measurable facts.
Common legal theory says that we can not do that. Fair use is inherently subjective and ruled on a balance of interests between copyright holders and the public good. The public good in turn is also extremely hard to define, and is usually seen as one of those things we know when we see it but can't attribute to logically consistent rules.
So this is a good example of what I'm talking about. You're talking about the difficulty of making a fair use determination, but the question in most of these cases isn't whether a specific action is fair use, it's whether any of the reasonable actions are. And you don't need to make an inherently subjective determination for that because the subjective cases are irrelevant if you can find any solid instance where the outcome isn't ambiguous.
The citation example makes the point pretty well. Suppose you make a citation -- this image is on page 34 of this book, using a standard machine-readable citation format.
There are multiple things the user and the user's browser could do with that information. It can show you links to stores where you can buy a print edition of that book, or it can look up the page in a location index and find electronic sources for the content of that page. Some of those sources and some of the uses of the content are plausibly unambiguous cases of fair use. Some of the sources and uses are plausibly unambiguous cases of piracy. They may even be the same sources but different uses.
If you want to evaluate one of the individual cases then you may have to make a complicated fair use determination, but we're not talking about an individual user, we're talking about the person providing the citation. Whether their intent is facilitating users buying the book, or using it in a clear case of fair use, or using it in a clear case of piracy, their action is the same. The action itself doesn't reveal their intent. You can't make the determination based on that because you don't know it.
The difference between this and the murder example is that the defendant's action isn't the directly prohibited thing. If you intentionally kill someone, that's what murder is. If you hire someone else to do it, you're still clearly intending that outcome.
The analogous thing would be selling weapons. Your obvious intent is to sell a knife, not to have someone murdered. That may secretly be your true motivation, but without any additional evidence of that there is no way to know, and certainly at least some of the people who sell weapons do so without the intent that they be used to commit murder.
It can be impossible to determining intent in some cases but that has not stopped law writers and politicians from defining intent and guilt in the absent.
The pirate bay case was actually a such example. The law that the judges cited in the case was based on the concept that if the majority usage of a tool is illegal then the owner of said tool can be held as an accomplish. The background text of that law was biker bars. The politicians wanted a way to confiscate the buildings, so they created the law. No intent needed of the owner, only establishing that the primary usage of the "tool" illegal and there you go. If you had a gun shop and the primary customers you got was murderers you could in theory be charged with assistance of murder in each case that the police can guess is likely to have happened. The pirate bay case also established that someone can be charged with with assistance even if the "original case" has not been proven.
Not saying any of that is good. The law is ugly, inconsistent and full of subjective aspects.
> The pirate bay case was actually a such example.
The pirate bay isn't in the US.
And in general, the fact that some bad laws exist that violate the general principles the legal system as a whole operates under is no excuse for condoning such laws or not construing them as narrowly as possible to mitigate the damage done to the justice system by naked populism like that.
If there are so many marijuana users that the majority of pipes sold are used for marijuana rather than tobacco, it makes absolutely no sense to punish the people selling pipes rather than either punishing the people actually using marijuana or just legalizing marijuana.
Common legal theory says that we can not do that. Fair use is inherently subjective and ruled on a balance of interests between copyright holders and the public good. The public good in turn is also extremely hard to define, and is usually seen as one of those things we know when we see it but can't attribute to logically consistent rules.