For all that Gigerenzer is a giant in social psychological research, the article doesn't half sound like two fields talking past each other. The entire purpose of behavioural economics is not to reinvent Gigerenzer's own field but to point out that humans frequently deviate from "rational expectations" outcomes predicted by orthodox economic models. Modelling deviations from rational choice theory is not "all that keeps it erect", it's its raison d'etre in critiquing a field where rational choice theory and unsystematic error is the default assumption. The crux of the "great rationality debate" is that Kahnemann is talking about rationality as "making correct predictions with random error" (or in terms of policy implications, "making predictions which lead to preferable outcomes to those which could be achieved by any other conceivable model") and finding examples where humans do not do this, whereas Gigerenzer is talking about rationality in terms of whether human intuitions and heuristics are justifiable in an evolutionary sense (and improvable upon by learning).

Gigerenzer is undoubtedly correct that Bayesian reasoning is something that can be learned by many people, and yet all that Kahnemann needs for the implications of his statement that "the human mind is not Bayesian at all" to be relevant in behavioural economics terms is for some portion of the population to reach systematically different conclusions from the correct Bayesian one using an inferior heuristic. (A point Gigerenzer essentially demonstrates by citing a study which show how outcomes improved after gynecologists already motivated to make correct predictions were taught Bayesian reasoning). Perhaps it's sloppy wording on the part of Kahnemann that Gigerenzer is taking exception to, but the core claim is not that humans cannot learn statistics, but that at a population level, some humans will continue to rely on less accurate heuristics which deviate from those predicted by rational expectations models in a systematic [and predictable] manner which are not simply eliminated over time due to financial incentives to be correct.

The one claim which really ought to be of serious concern to behavioural economists is that their experimental studies frequently mistake random error (acknowledged by 'rational expectations' orthodox economics) for systematic error, so it's perhaps unfortunate that the Kahnemann example Gigerenzer highlights in this paper as not being replicable is an abstract demonstration of the availability heuristic with zero direct economic implications.