The human connectome displays nontrivial large-scale organization despite being assembled through decentralized, local biological processes. Most generative models reproduce selected connectomic features by invoking global optimization principles, predefined wiring targets or developmental templates. This leaves unresolved which properties of the connectome are genuine consequences of local interactions and which require additional mechanisms operating beyond local scales. We introduce a simulation framework conceptually aligned with recent theoretical results showing that global coherence can arise from local compatibility alone. Networks are generated exclusively through local constraints: nodes interact within bounded spatial neighborhoods, edge formation is probabilistic and local, and incompatible configurations are suppressed without reference to any global objective, target topology, or long-range coordination. Ensembles of simulated networks are compared with empirically reported human connectome descriptors using quantitative statistics and qualitative structural criteria. Several mesoscopic properties, including high clustering, modular organization, motif enrichment and short-range wiring bias, emerge robustly under local interaction rules and compatibility. In contrast, other features such as absolute connectivity scale, rich-club organization and long-range hub-to-hub coupling, systematically diverge from empirical values. Unlike optimization-based or template-driven models, our framework does not aim to reproduce the full connectome. Instead, it identifies which properties are structurally implied by locality and which remain underdetermined, providing a complementary explanatory perspective. Our results support a principled classification of connectome properties according to their dependence on local compatibility constraints, clarifying the explanatory scope and limits of decentralized network formation, and suggesting several directions for further work.