Graph neural networks (GNNs) are the dominant paradigm for classifying nodes in a graph, but they have several undesirable attributes stemming from their message passing architecture. Recently, distillation methods succeeded in eliminating the use of GNNs at test time but they still require them during training. We perform a careful analysis of the role that GNNs play in distillation methods. This analysis leads us to propose a fully GNN-free approach for node classification, not requiring them at train or test time. Our method consists of three key components: smoothness constraints, pseudo-labeling iterations and neighborhood-label histograms. Our final approach can match the state-of-the-art accuracy on standard popular benchmarks such as citation and co-purchase networks, without training a GNN.