The COVID-19 pandemic has claimed millions of lives, spurring the development of diverse forecasting models. In this context, the true utility of complex spatio-temporal architectures versus simpler temporal baselines remains a subject of debate. Here, we show that structural sparsification of the input graph and temporal granularity are determining factors for the effectiveness of Graph Neural Networks (GNNs). By leveraging human mobility networks in Brazil and China, we address a conflicting scenario in the literature: while standard LSTMs suffice for smooth, monotonic cumulative trends, GNNs significantly outperform baselines when forecasting volatile daily case counts. We show that backbone extraction substantially enhances predictive stability and reduces predictive error by removing negligible connections. Our results indicate that incorporating spatial dependencies is essential for modeling complex dynamics. Specifically, GNN architectures such as GCRN and GCLSTM outperform the LSTM baseline (Nemenyi test, p < 0.05) on datasets from Brazil and China for daily case predictions. Lastly, we frame the problem as a binary classification task to better analyze the dependency between context sizes and prediction horizons.