Right, the whole point is that there's a lot of studies, and professional web designers don't seem to use them.
As someone who worked in the area of Intelligence training I am very, very skeptical. For example, there was a burst of optimism about training working memory through Dual N-Back tasks, bought about by a revolutionary paper from Jaeggi et al. Then... not quite nothing but close.
I suspect there's a reason that no braining activity, ever, has been consistently shown to improve intelligence at the construct level. It may be that more specific capacities related to intelligence (like working memory) are improved, and that these affect life outcomes and practical capacity to grasp concepts etc, but this has yet to demonstrated to my satisfaction.
I'm not convinced that improving calibration will not improve accuracy because predictions are often nested within other predictions. For example, suppose we are trying to make a prediction about P, and the truth or falsity of Q, R and S are relevant to the truth of P in some respect. We might use as a basis for guessing P that we are ninety five percent confident in our guesses about Q, R & S, (suppose the truth of all three would guarantee P). Now suppose we become less confident through better calibration and decide there is only a 70% chance that Q, a 70% chance that R and a 70% chance that S, leading to a compound probability of less <50%. Thus overall accuracy can be improved by calibration.