Vision Transformers rely on positional embeddings and class tokens encoding fixed spatial priors. While effective for natural images, these priors may be suboptimal when spatial layout is weakly informative, a frequent condition in medical imaging. We introduce ZACH-ViT (Zero-token Adaptive Compact Hierarchical Vision Transformer), a compact Vision Transformer that removes positional embeddings and the [CLS] token, achieving permutation-invariant patch processing via global average pooling. Zero-token denotes removal of the dedicated aggregation token and positional encodings. Patch tokens remain unchanged. Adaptive residual projections preserve training stability under strict parameter constraints. We evaluate ZACH-ViT across seven MedMNIST datasets under a strict few-shot protocol (50 samples/class, fixed hyperparameters, five seeds). Results reveal regime-dependent behavior: ZACH-ViT (0.25M parameters, trained from scratch) achieves strongest advantage on BloodMNIST and remains competitive on PathMNIST, while relative advantage decreases on datasets with stronger anatomical priors (OCTMNIST, OrganAMNIST), consistent with our hypothesis. Component and pooling ablations show positional support becomes mildly beneficial as spatial structure increases, whereas reintroducing a [CLS] token is consistently unfavorable. These findings support that architectural alignment with data structure can outweigh universal benchmark dominance. Despite minimal size and no pretraining, ZACH-ViT achieves competitive performance under data-scarce conditions, relevant for compact medical imaging and low-resource settings. Code: https://github.com/Bluesman79/ZACH-ViT