We’ll see how this develops — see my comments to Leigh’s blogpost for my (evolving) view. I think, as I say in this piece, that one way to see things is that System 3 provides the temporal dimension that, inherently, neither System 1 nor System 2 have. They take current inputs, and either choose a quick shortcut, or perform a long calculation to produce a decision. But they do not, themselves, take into account possible alternative future states.
System 3 is capable of taking current inputs and produce possible future states, which can then also be supplied to Systems 1 and 2.
(I am aware of the highly metaphorical nature of this view, but that is true for any discussion involving Systems 1 and 2 as well.)