In AdS/CFT correspondence, one mostly studies the case with AdS$_5 \times$ S$_5$ on the string side and $4$d $\mathcal{N}=4$ Super Yang-Mills on the gauge field theory side. Real-world observations show that gravity occurs in a $4$-dimensional Universe, possibly with compact dimensions. Then would it not be more interesting to look at correspondences between AdS$_4$ and $3$d CFT? In that way, one would hope to be able to describe $4$d quantum gravity with a $3$d Yang-Mills theory or something. Maybe the reason is that this implies giving up on the Standard Model, but when I think about it I do not see an obvious reason why this should be necessary at first (maybe in latter stages though).
Note that I am putting aside for now the fact that AdS space does not seem to reproduce our Universe. Also, I am aware that there actually exists such dualities in the literature, but they seem more academic-oriented, in the sense that their aim is not to describe reality (maybe I am wrong?). And of course I can imagine the $\mathcal{N}=4$ being useful for practical purposes if one tries to describe e.g. QCD with string theory.