I immediately surrender any claims to having given perfect types to the functions I would like to have. All I want is to have things that work somewhere at hand, and not at all to have perfect things nowhere. Nevertheless, I am going to reply to your objections.
* Group a collection by an equivalence relation:
classify ∷ Ord π ⇒ (a → π) → [a] → [[a]]
If the provided function is indeed an "equivalence relation", shouldn't the type be Eq π ⇒ (a → π) → [a] → [[a]], which is basically Data.List.groupBy? On the other hand if the resulting list is supposed to be ordered, most practical applications will probably use a set or a map anyway.
`Data.List.groupBy` detects only adjacent equivalent elements. The intention here is to detect distant equivalent elements as well. You may see a more detailed explanation and examples here: https://stackoverflow.com/questions/8262179. See also previous discussion here: https://mail.haskell.org/pipermail/libraries/2020-August/030736.html. You may also see from these sources that it is not trivial to define this function without the `Ord` constraint. In more detail: there are two versions, one of which requires only `Eq` and runs in _n × m_ time, and the other requires `Ord` and runs in _n × log n_ time. Neither is clearly better. The most precise and informative type for the result seems to be `[NonEmpty α]`. I do not see how `Set` or `Map` would be more suitable.
* From a finite map, get a map from its range to its fibers:
fibers ∷ (Ord k, Ord v) ⇒ Map k v → Map v (NonEmpty k)
Why NonEmpty, and not Set? Or any Monoid? And more importantly, who are we to decide? Again, the cost difference between maintaining and re-discovering one "standard" vs. re-implementing something more precisely suited to the task at hand via (e.g.) Data.Map.foldMapWithKey doesn't seem worth it.
Because a fiber is non-empty. Ideally, sure, I would like `(k, Set k)`. The remainder of the quote would be very hard to substantiate. I evaluate the cost and the benefit differently, that is all.
* Put a type into the diagonal of its square:
diagonal = λx → (x, x)
Now this might fit into Data.Tuple. Then again, it's faster and more self-documenting to re-implement it at hoc than to remember a name.
Also, this (again) is less useful than it seems. It will almost always require an application of uncurry as well, which makes the program harder to understand. Sometimes it's better to replace both with a single application of the Monad instance of (->) – or with the "real" function.
For example:
uncurry (+) . diagonal ≡ join (+) ≡ \x -> x + x ≡ (2*)
I added this for a joke. It has been discussed previously at hilarious length. See: https://mail.haskell.org/pipermail/libraries/2018-October/029051.html https://mail.haskell.org/pipermail/libraries/2019-July/029744.html https://mail.haskell.org/pipermail/libraries/2020-September/030789.html Surprizingly, many high profile Haskell programmers agree that it is useful.
It is unfeasible to put them into the standard libraries. _(Attempts were made.)_
This sounds like the maintainers of the standard libraries had their own objections. I suspect some of them might be similar to the ones above. Which leads me to suspect you might not have taken their feedback to heart. Which might in fact be the biggest hurdle on getting your code accepted into a library.
Turns out your objections mostly come down to evaluation of usefulness, which would be very hard to substantiate by evidence, especially since usefulness is potential as much as it is actual.