You are absolutely correct that the picture shown is in equilibrium. The pressure at the top and sides need not be 0, but it will be less than the pressure on the bottom by the amount of the weight of the fluid. So the net force and net torque on the fluid is zero and there is no tendency to accelerate or rotate. This indeed means that the fluid in this configuration is in equilibrium.
There are two types of equilibrium: stable and unstable. Although tisthis configuration is an equilibrium it is an unstable equilibrium. Specifically, this configuration is subject to the Rayleigh-Taylor instability
https://en.m.wikipedia.org/wiki/Rayleigh–Taylor_instabilityRayleigh-Taylor instability
Basically, if a small parcel of the water descends and is replaced by an equal volume of air going up, the potential energy of the system is reduced. This means that the system will not tend to return to the original configuration. So any deviation from the perfect equilibrium state will grow exponentially, regardless of how minuscule* it is initially.
Since there is always some small deviation, the fluid deforms, forms drops, and falls down as expected from common experience.
*Surface tension can actually stabilize very small deviations in some fluid interfaces.