Learning curve is a very high cost by itself; HKP is
the reason Haskell is notoriously difficult to learn. (Compare to Elm, which is also a referentially transparent typed ML with parameteric polymorohism and row types, with nearly identical syntax to Haskell...and which is notoriously
easy to learn.) Haskell beginners don't need to get into GADTs and type families and higher-ranked types, but HKP is practically unavoidable on the road to understanding a Haskell program that prints Hello World.
Another cost is in standard library complexity. You can't have HKP and not have a stdlib with Functor/Monoid/Monad etc. As Scala has demonstrated, if you have HKP but don't put these in the stdlib, a large faction will emerge pushing an alternative stdlib that has them. A larger, more complex stdlib is a cost, and so is a fractured community and ecosystem; HKP means you'll have to pick one of those two.
API design is another. Without HKP you write a function that takes a List. With HKP you now need to decide: should it actually take a List, or is it better to take a Functor/Semigroup/Monoid/Applicative/Monad instead?
If you choose one of the more generic ones, now it takes more mental steps to collapse the indirection when reading it. (1. I have a Maybe Int. 2. This function expects an `s`. 3. `s` is constrained by `Semigroup s`. 4. Can I pass a Maybe Int to something expecting a Semigroup? Compare to "This function takes a `Maybe a`", and multiply that small delta of effort by a massive coefficient; this is something everyone who reads these types will do many, many times.)
This indirection also has implementation costs; in theory you could make docs and error messages about as nice if HKP is involved as if not, but there's an implementation cost there, and it seems like it must be pretty steep if you stack up languages with HKP and their quality of error messages and docs against other typed languages that don't.
So I'd say it's one huge cost (automatic induction into the highest tier of learning curve steepness), one big cost (either a larger and more complex stdlib or fractured community), and several smaller costs with high coefficients because they come up extremely often.
Yeah there are benefits too, but I don't think they get anywhere near outweighing the costs.