Of course this all depends on jurisdiction, but e.g. in the US for example fair use does not show up [oops, see note] in the limitations and exceptions in the copyright definition (like e.g. government use does), but relies on case law, the "fair use doctrine". This means quite literally it is a framework for understanding the defence of a particular use based on precedent: the defendant(s) argued it.

It's a bit of a quibble to differentiate between allowable infringement or exception, here, so i've edited original.

[note: 0xcde4c3db points out correctly that it does actually show up since 1976, but in a way the defers much of the definition back to case law, so same effect]

Maybe there's some nuance of your description that I'm missing, but fair use is codified as a limitation to copyright in US statute (although not until 1976) [1]. Application of it to any given situation is still heavily dependent on case law, though.

[1] https://www.law.cornell.edu/uscode/text/17/107

Fair enough - I had forgotten that quirk in the US situation, it was added to statute in a way that doesn't really define it, so you are back to case law.

I think it makes a difference, because it shifts the burden of proof. If fair use is a kind of infringement, then it’s up to the “infringer” to prove fair use. I think that’s ethically and legally backwards: the copyright holder should have to prove that the use was not fair.

Ethics aside, and again US specific, but the supreme court literally defines it as an affirmative defence.

Even this is a bit murky though, as a district court has argued it goes beyond that.

and it seems unlikely to benefit society to let Microsoft and Google to hoover up 100% of creative works, then use that to compete with everyone in that industry to such an extent they can no longer make a living

Fair use is a legal defense that requires you to pass multiple tests. It's not a "thing" that you can just assert all AI training is and expect people to believe you.