Actually it is more about kinetics than thermodynamics. Folded inner membrane of mitochondria allowed more surface area for biomolecule production/reaction/consumption, which added to efficiency( and complexity )of mitochondrial ancestor survival skill that became incorporated into gene with evolution. Before mitochondria was captured by endosymbiosis, their role was like present day mesosomes of bacteria, not only to obtain high amount of reactant-product exchange surface area, but also to hold specialized organelle, for metabolism, reproduction etc. When it was captured, the same trait allowed rapid chemical exchange between cytoplasm of proto-eukaryote and would-be mitochondrion.

also remember, Mitochondria membrane system is selectively permeable, and selective transport in rapid time is possible only if surface area of the organelle per unit volume is folded. same trend is seen in thylakoids of chloroplasts. Why the outer membrane is smooth and inner one is rough can not be easily answered, but it might be due to fluid-mechanical viscosity/surface tension constraints of locomotion on morphology of modern mitochondria,s predecessor. Also note, the inner membrane is selectively permeable, but outer membrane is not so much.