To clear up a probably small thing, this is the third time I saw this quoted in the forum. I forgot but someone even attributed it to a possible connection with hexagonal formation. 7+/-2 is a 1956 study by Miller specific to visual short term memory which some argue that it lacks backing. More recent research by Cowan (2001, 2005, 2010) and others argue this number to be 4 based on rate distortion theory and it is a more accepted generalization in Human Memory field. In either case, this may be considered as a characteristic of the architecture rather than a limitation. In my perspective, you can alter these characteristics which potentially costs you in other forms. These are sort of reference points in cognitive sciences that whatever model you are working on should converge to if the goal is to simulate human behavior. If you are only after AGI bypassing biological behavior maybe you can ignore these constraints.
To answer your original question, I do not think HTM is there yet to provide explanations to high level cognitive phenomenon such as the validation of these kind of limits. However, you can speculate about low level phenomenon such as a capacity of a single cortical column or psychological constraints on sequence learning on the level of a cortical column. But then I am not aware of any psychological studies that dwell on this sort of lower level phenomenon and I am not sure if this is possible without some elaborate brain imaging. Take this with a grain of salt.
You actually poked my current problem. How do I tie up psychological studies with HTM to converge on biological behavior? As it is also valuable on top of neurobiology. Nengo, the closest thing to HTM considering the emphasis on neurobiological plausibility, also strives to concur with psychological phenomenon.