"They're a necessary workaround to do some stuff in pure functional languages"

This isn't actually true. You can still write imperative programs in a pure FP language. The most obvious way is to write your code in continuation passing style and pass the new state of the world to each continuation; taking the implicit state changes of an imperative language and making them explicit.

The real reason for using monads is that the scheme I just described is inhumanly complicated. Monads are a much more structured way of doing the same thing. Instead of writing these state passing CPS functions, you write functions that build them for you. A consequence of this is that monads perform much the same function as macros in Lisp; they are programs that build programs.