This question of mine has been marked as duplicate. I tried to argue my case in the text of my question but it seems this forum is more appropriate. My apologies if this is not so.
It is a definite duplicate of Q10075 which has rather low quality answers: no, superstrings can't predict only 4 dimensions are not compactified. My question was also marked as a duplicate of Q10651. It did not seem obvious at first as superstrings were not discussed at all there but I shall thank the moderator for the pointer because one of the answer, A10723, cites a paper "Relaxing to Three Dimensions by Karsh and Randall which, although it is far too advanced for my current understanding of physics, seems to answer my question with a "yes". Here is the abstract:
We propose a new selection principle for distinguishing among possible vacua that we call the “relaxation principle.” The idea is that the universe will naturally select among possible vacua through its cosmological evolution, and the configuration with the biggest filling fraction is the likeliest. We apply this idea to the question of the number of dimensions of space. We show that under conventional (but higher-dimensional) FRW evolution, a universe filled with equal numbers of branes and antibranes will naturally come to be dominated by 3-branes and 7-branes. We show why this might explain the number of dimensions that are experienced in our visible universe.
From the page of the paper, I clicked on "cited by" and there seems to be a handful of papers arguing the same point, but again I am at the level of matching buzzwords! As for the answer itself which quotes this paper, it is again of low quality as it adds no value at all to the paper.
To summarise, we are in a situation where existing answers seem either wrong, or are useless to me, and by extension to anybody who is not a postgraduate-level physicist. May I enquire what could be done?