public <T> higherOrderFunction(Function<T> f) throws whatever f throws { }

I can write a method that takes in a function object that throws zero checked exceptions. I can write a method that takes in a function that throws exactly one type of checked exception. I can write a method that takes in a function object that can throw two types of checked exceptions. And so on. But this involves lots of copy-pasting, which is the opposite of abstracting.

Checked exceptions are not first-class citizens in the language (see https://en.wikipedia.org/wiki/First-class_citizen). Unlike return values, I can't, for instance, in the general case assign the possible checked exception thrown by a method to a variable without losing type information. To do so would require sum types, a feature which most popular languages don't have.

On the other hand, if I create a class like IO<T>, which represents a possible return value of T or an IOException, then that is first class in the language and I can do anything with it that I can do with any other first-class value in the language.