The way I think about it is that the general monadic structure is that the results of an operation can cause new operations to happen with equivalent complexity

The way I think about it is that the general monadic structure is that the results of an operation can cause new operations to happen with equivalent complexity. This is exactly what "flat map" is. So what the "IO monad" in Haskell represents is the general principle across programming languages where you can, say, read a file, then for each line in the file read another file or otherwise do additional I/O -- and this can spiral out in an unbounded fashion. As developers we can observe the monadic structure of operations everywhere (and generally seek to avoid it! Monads are fundamentally too powerful!) But whether it is worth encoding the general idea of monadic structures into the type system is a separate question. Haskell says yes, most others say no. There are good reasons both ways. (One underappreciated reason is that exposing a hierarchy of typeclasses/traits introduces API stability considerations. When Applicative was inserted in between Functor and Monad in Haskell, the whole ecosystem had to be updated.)