Despite massive investments in scale, deep models for click-through rate (CTR) prediction often exhibit rapidly diminishing returns -- a stark contrast to the {predictable scaling laws} seen in large language models (LLMs). We identify the root cause as a {fundamental} \textit{structural misalignment}: {standard} Transformers assume sequential compositionality, whereas CTR data demand combinatorial reasoning over {heterogeneous} fields. To restore alignment, we introduce the \textbf{Field-Aware Transformer (FAT)}. {By reconstructing the standard Transformer block with field-centric parameters, FAT achieves \textit{structured expressivity}, {fundamentally shifting the model complexity dependence from the total vocabulary size $n$ with the number of fields $F$ ($n \gg F$).}} Crucially, to decouple model capacity from field cardinality, FAT employs a {Basis-Composed Hypernetwork} to synthesize field-specific parameters from shared bases, further reducing parameter complexity. {Theoretically, we ground this scaling behavior through a formal scaling law based on Rademacher complexity. Empirically, FAT outperforms exisiting state-of-the-art methods with up to \textbf{+4.38\%} AUC improvement, and delivers \textbf{+2.33\%} CTR and \textbf{+0.66\%} RPM in live production.} Our work establishes that scalable recommendation arises not from size alone, but from \textit{structured expressivity} -- architectural coherence with data semantics.