Surface roughness ($R_a$) is a central quality indicator in precision CNC grinding, yet it is measured offline, after machining. Predicting $R_a$ from machine-internal spindle signals offers process-signal-based workpiece quality prediction with the potential for in-process monitoring. We argue that model selection for such soft sensors must satisfy three requirements jointly: signal, robustness beyond the training campaign, and budget on a CPU-only edge gateway, including the feature-extraction cost of classical pipelines. We evaluate feature-based classical regressors, end-to-end sequence models (1D CNN, BiGRU), and the kernel-based MultiRocket transform on the High Precision CNC-Grinding Roughness dataset (20 workpieces, two campaigns) under leave-one-workpiece-out and cross-campaign protocols with strictly fold-internal preprocessing, workpiece-level bootstrap confidence intervals, and an edge-oriented deployment benchmark that charges feature extraction to the classical path. Within the known campaigns, the best models reach an MAE of 0.17 $\mathsf{\mu }$m ($R^2\approx 0.5$), 44% below a mean-prediction baseline. Under campaign shift, no model retains practically useful accuracy and the within-distribution ranking partially inverts. We trace this to a strong campaign-level target shift (Cohen’s $d=3.24$) perfectly confounded with the only varying process parameter, so that within-distribution accuracy may reflect campaign identity rather than a campaign-invariant process–roughness relationship. The compact CNN is the cheapest complete pipeline (5.4 ms model path per workpiece), whereas the evaluated library-level MultiRocket implementation costs 7.0 s. Each family fails a different requirement; we give guidance on which deployment claims the data currently support.