Spontaneous perforation of amphiphilic membranes is important in both living matter and technology because of an impact on functions of biological membranes and shape transitions of self-assembling structures. Nevertheless, no definite molecular mechanism has been established so far even for simple ionic surfactant systems. We show that spontaneous perforation of a bilayer formed by an ionic amphiphile is driven by electrostatics. Creation of large pores with a concave convex geometry of the rim is promoted by lower electrostatic free energy than that for a flat nonperforated bilayer. The opposite effect comes from the elasticity of the hydrocarbon tails of the amphiphile that prefer flat geometry of a nonperforated bilayer. The balance between electrostatics and tail deformation controls the appearance of pores; this balance is modulated by added salt that screens the electrostatic interactions. We illustrate the proposed mechanism with the aid of classical aggregation model that has been extended by including an analytical description of the electrostatic contribution for the toroidal rim of a pore. Numerical solution of the linearized Poisson-Boltzmann equation confirms the role of electrostatic forces in formation of pores. For the ionic surfactants of C(n)TAB family, we predict shape transitions including bilayer perforations and formation of branched micellar networks induced by changing salinity or temperature and demonstrate the effect of surfactant's molecular parameters on these transitions.