The two most important ingredients to static assignment are the assumption of equilibrium and the assumption of steady state, i.e. steady state OD flows. Equilibrium is plausible; and variants of it are currently also used in simulation approaches. The assumption of steady state in contrast leads to the unrealistic distortions of the traffic flow dynamics that we have discussed earlier.
Once these assumptions are made, it turns out that one can formulate the resulting problem as a constrained minimization problem. Under weak additional assumptions (strict monotonicity of the cost-flow-relation), the problem has a unique solution in the link flows. This is a very desirable property, since the solution will not depend on the particular computational method that is used. This is very different from simulation, and certainly an important reason why static assignment is liked so well.