Tabular learning is still dominated by row-wise predictors that score each row independently, which fits i.i.d. benchmarks but fails on transactional, temporal, and relational tables where labels depend on other rows. We show that row-wise prediction rules out natural targets driven by global counts, overlaps, and relational patterns. To make "using structure" precise across architectures, we introduce grables: a modular interface that separates how a table is lifted to a graph (constructor) from how predictions are computed on that graph (node predictor), pinpointing where expressive power comes from. Experiments on synthetic tasks, transaction data, and a RelBench clinical-trials dataset confirm the predicted separations: message passing captures inter-row dependencies that row-local models miss, and hybrid approaches that explicitly extract inter-row structure and feed it to strong tabular learners yield consistent gains.