> why `m a -> (a -> m b) -> m b` but not something else?

it's basically continuation-passing-style (`a -> m b` is the "continuation"), you might as well ask "why can you represent so many control-flow things using CPS?". idk why, but you can!

from another angle, you could compare Monad with the less powerful Applicative. a formulation[0] that's easier to parse than the usual one[1] is:

  class Functor f => Applicative f where
    unit :: f ()
    pair :: f a -> f b -> f (a, b)

if you're familiar with JS Promises, a rough analogy would be

  >>=  (Monad)        Promise.then
  pair (Applicative) ≈ Promise.all
  unit   (Applicative) =
  return (Monad)       = Promise.resolve

ignoring parallelism, you can implement Promise.all using Promise.then, but not the other way around.

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[0] Called "Monoidal" here: https://stackoverflow.com/q/45267953 [1] https://en.m.wikibooks.org/wiki/Haskell/Applicative_functors...