Subword tokenizers are optimized for compression, but their boundaries also define the prediction units seen by a language model. We introduce StructPiece, an unsupervised tokenizer that enforces Unicode Extended Grapheme Cluster (EGC) boundaries and biases merge induction toward corpus-induced affix patterns without external resources. Across nine languages and five scripts, StructPiece exposes a compression–representation frontier: it produces higher-fertility segmentations with worse bits-per-character but substantially lower token-level perplexity under matched architectures, vocabulary sizes, and token budgets. Fixed-budget, granularity-matched, and component ablations show that the effect is not explained by token count alone; structural vocabulary alignment is further tested through LLaMA-3.2-1B vocabulary surgery, replacing its 128k vocabulary with 32k StructPiece tokens via mean-pooled initialization. StructPiece recovers 89.4% of baseline zero-shot reasoning performance across morphologically rich languages (X-CSQA) after 2.6B adaptation tokens, compared with 76.4% recovery for naive BPE surgery under the same checkpoint. Furthermore, structurally aligned tokens produce higher mean-pooled embedding cosine coherence, suggesting better-conditioned vocabulary projections. These results suggest that token boundaries act as a controllable structural bias influencing prediction granularity and vocabulary adaptation. StructPiece is available at https://github.com/submissionemnlp26-beep/structpiece-code.