Atomic-vapor density change due to light induced atomic desorption (LIAD) is studied in paraffin-coated rubidium, cesium, sodium, and potassium cells. In the present experiment, low-intensity probe light is used to obtain an absorption spectrum and measure the vapor density, while light from an argon-ion laser, array of light emitting diodes, or discharge lamp is used for desorption. Potassium is found to exhibit significantly weaker LIAD from paraffin compared to Rb and Cs, and we were unable to observe LIAD with sodium. A simple LIAD model is applied to describe the observed vapor-density dynamics, and the role of the cell's stem is explored through the use of cells with lockable stems. Stabilization of Cs vapor density above its equilibrium value over 25 min is demonstrated. The results of this work could be used to assess the use of LIAD for vapor-density control in magnetometers, clocks, and gyroscopes utilizing coated cells.