While learning-based channel predictors show promise for reducing pilot overhead in next-generation orthogonal frequency-division multiplexing (OFDM) systems, the lack of principled performance benchmarks prevents rigorous assessment of their proximity to theoretical limits. We derive a closed-form linear minimum mean-square error (LMMSE) benchmark for strictly causal pilot-to-prediction (P2P) in frequency-selective OFDM systems. For Gaussian wide-sense stationary uncorrelated scattering (WSSUS) channels, this benchmark equals the Bayesian Cramér–Rao bound (BCRB), decomposing irreducible error into temporal prediction and pilot-induced estimation components with closed-form eigenvalue expressions. Evaluating five neural architectures, we find that Transformer and state-space model (SSM) closely track the LMMSE benchmark on COST 259 channels, while long short-term memory (LSTM) and Autoformer exhibit larger gaps. Crossformer operates below the benchmark at most tested speeds, consistent with nonlinear exploitation of non-Gaussian structure in finite sum-of-sinusoids (SoS) channel models, though it exhibits elevated gaps at low Doppler; a reduced-capacity ablation indicates a capacity–architecture interaction. On 3rd Generation Partnership Project (3GPP) TR 38.901 Tapped Delay Line-A (TDL-A) channels, both Transformer and Crossformer exhibit strictly positive gaps across all tested speeds. This demonstrates that while nonlinear methods can surpass the linear benchmark, Transformer and SSM have closely approached it, implying that further gains depend primarily on pilot density, signal-to-noise ratio (SNR), or prediction horizons.