"Put the saucepan on the stove."
Translation:Поставь кастрюлю на плиту.
I think that the accusative case is correct. Extending your suggested reasoning, the prepositional case would be used only if there were no movement. If I translated, e.g., "Yesterday I walked to school," I would use the accusative "в школу" even though I were в школе after the action ended.