Battery energy storage systems (BESS) rely on accurate electricity price forecasts to maximize arbitrage profits in day-ahead markets. We examined whether specific forecasting models, ranging from statistical benchmarks to machine learning methods, consistently deliver superior financial outcomes for storage operators. Using real market data from the Italian day-ahead electricity market over 2020–2024, we compared univariate singular spectrum analysis (SSA), ARIMA, SARIMA, random forests, and a 30-day simple moving average under a unified trading framework. All models were evaluated based on their ability to generate arbitrage profits. Univariate SSA clearly outperformed all alternatives, achieving on average 98% of the theoretical maximum profit while maintaining the lowest forecast error. Among the other models, simpler approaches performed surprisingly well: they achieved comparable, if not superior, profit performance to more complex, hour-specific, or computationally intensive configurations. These results were robust to plausible variations in battery parameters and retraining schedules, suggesting that univariate SSA offers a uniquely effective forecasting solution for battery arbitrage and that simplicity can often be more effective than complexity in operational revenue terms.