I think the issue is with checked exceptions as a solution to how to declare this signature, or at least with how they are designed in Java: if you add a new exception to the signature, every downstream call site needs to change, recursively.

This means it is impossible to add new exceptions to library methods without breakage, and even in your own code it may mean hundreds of changes throughout your code to add a new exception type.

Rusts solution seems to have improved this conundrum, where you can describe how to map the new error into an existing hierarchy in a single or a few places instead of at every call site

From a type theory perspective if you want to track exceptions as return values you want a composable container class (best case, a full monad) so that you aren't writing a lot of ad hoc code every time to handle them.

That's a big problem with Java's checked exceptions, it's not very composable and flow control can just stack up into deeper and deeper "waterfalls" of code rather than simpler pattern matching. (To be fair that's a big problem with exceptions in general as "flow control", they aren't very composable.)

Something like an Either monad in a language with sum types can be a great way to describe errors/exceptions usefully as return types. From a type theory perspective, checked exceptions can be seen as a hack for a language that doesn't support sum types and doesn't have great native monad binding.

> and not documenting those in the function signature is absurd

Exceptions can be thrown from anywhere. That's the documentation.