Kinetic electron-emission yields gamma from swift ion penetration of solids are proportional to the (electronic) stopping power gamma approximately Beta-S*, if the preequilibrium evolution of the charge and excitation states of the positively charged ions is taken into account. We show that the concept of the preequilibrium near-surface stopping S* can be applied successfully to describe the dependence of the ion-induced electron yields on the projectile atomic number Z(P) and on the charge states q(i) of the incoming ions. We discuss the implementation of this concept into Schou's transport theory after having presented a summary of recent results on the projectile- and charge-state dependence of forward and backward electron yields gamma(F) and gamma(B) and the Meckbach factor R = gamma(F)/gamma(B). A simple extension of the yield equations is proposed and several assumptions are justified by investigating the "transport factor" beta, the energy spectrum of directly ejected recoil electrons and the evolution of ionic charge state inside solids. Estimates of the energy-loss fraction leading to electron emission and the effective charges of the ions near the surface allow a quantitative description of the Z(p) dependence of the electron yields.