Saudi Arabia, long accustomed to any reforms progressing at a snail’s pace, has approved a radical plan to restructure its economy to bring about greater diversification and transparency. At the heart lies oil giant Saudi Aramco, of which the kingdom plans to privatize up to 5% in what would be the largest IPO in history.

The extent of the ambitions are unquestionable, but is such a wide ranging and swift shakeup really feasible? Can the social bargain upon which the kingdom’s...