The concept of reversibility in complex chemical reaction networks has recently been introduced in discussions concerning the origin of biological homochirality. In computational studies drawing on an analogy to recent experimental studies involving reversible crystallization processes, recycling of reaction educts has been suggested to provide a driving force for the spontaneous emergence of homochirality. We demonstrate here that reversible reaction networks closed to mass flow lead inexorably to a racemic state for thermally driven reactions, which must adhere to the principle of microscopic reversibility. This conclusion was reached for analogous "triangle reaction" networks studied by Onsager in 1931. Special cases such as photochemical reactions offer an exception that may have prebiotic relevance. Fundamental differences between physical and chemical systems are discussed in order to clarify the role of reversibility in each case.