I start with the Large $N$ QCD paper by 't Hooft. When 't Hooft published his paper on Large $N$ QCD it was clear why the string theory of hadrons due to Gabriele Veneziano could make sense. But at the same time, it was an end to strings as fundamental entities responsible for strong nuclear force. In fact, it turned out that the large $N$ QCD gives rise to Flux tubes and turned out as an effective field theory of QCD.
My question is, why don't we interpret AdS/CFT in the same manner, in the sense that the large $N$ limit of super Yang-Mills theory gives rise to a Stringy picture that is by definition only an effective field theory of the Super Yang-Mills in the large $N$ limit?
The fact that such duality is proven in that particular limit and not for arbitrary finite $N$ is the core of my question.