Assume that some human cognition is actually extended. What follows? A whole lot. Cognitive neuroscience is in trouble; computational psychology is partly misguided; and social psychology is in need of a change. (p. 1).The consequences of human extended cognition really depend a lot on more details of the view.
First of all, there is the question of how much "some" covers. If there is one human with an prosthetic device in which there is extended cognition, maybe not much changes.
Second, if we are talking about folk cognition in the way Clark does, at least at times, then it seems to me relatively unimportant that that extends. What the cognitive neuroscientists, computational psychologists, and social psychologists should worry about is whether or not scientific psychology extends. Or, at least, if the extension of folk cognition has these consequences, then this merits further argumentation.
Third, suppose one goes the route of thinking of the kind of cognition that extends as some form of "general liberal" cognition. This would be the kind of general cognition that is supposed to dodge objections to the equivalence of Inga-Otto by way of appeal to "coarse functional equivalence" (whatever that amounts to). Why not suppose that extant cognitive neuroscience, computational psychology, and social psychology are about/attend to these? After all, that's what Adams and Aizawa and Rupert have been pointing out. Extant cognitive psychology cares about things such as primacy and recency effects, the generation effect, and so on and so forth. No defender of EC has ever, to my knowledge, denied these claims. So, why would that change just because we find these new general psychological categories?
Fourth, Clark is among those who advocates a Complementary Version of Extended Cognition. That's the idea that, while there is some cognition that extends, there remains a "cognitive core" in the brain. If there is such a cognitive core, then why isn't cognitive neuroscience about this cognitive core? And, maybe current views in computational psychology and social psychology could just be focused on developing their views with the views of the cognitive core.
But, if you don't have these versions of EC, then you could get different consequences.