A forEach can easily return a transformed list of values.

  acc = []
  for el in values:
    acc.append(f(el))
  return acc

This hierarchy doesn't exist; you can pretty much implement any of them in terms of the others.

To make that untrue, you need to define very strict limits on what else your language can do.

(Sure, we produce a transformed list here through the use of side effects. But note that the original example sparking the claim that forEach can't do what map can was this:

  .forEach(() => button.click())

Side effects are clearly allowed.)