The dominant paradigm of local multi-agent systems -- orchestrated, enterprise-bounded pipelines -- is being superseded by internet-wide agent societies in which autonomous agents discover each other through open registries, interact without central orchestrators, and generate emergent social behaviors. We argue that governing such societies requires institutional design, not merely risk enumeration or process compliance. Applying Talcott Parsons' AGIL framework -- four functional imperatives (Adaptation, Goal Attainment, Integration, Latency) every viable social system must satisfy -- we derive a prescriptive sixteen-cell institutional architecture for internet-wide agent governance. Diagnostically applied to the OpenClaw ecosystem (250,000+ GitHub stars, 2M+ monthly users, 770,000+ registered agents) via a recursive sub-function analysis (64 binary indicators across 16 cells), we find at most 19% sub-function coverage (sensitivity range 17-30%) -- potential rather than operative capacity, since zero inter-cell coordination prevents existing infrastructure from participating in inter-pillar interchange. A complementary interchange media assessment finds zero of twelve inter-pillar pathways functional: the ecosystem has technical infrastructure but no active governance, no coordination layer, and no normative grounding, with the Fiduciary and Political pillars most severely underserved. Extending the diagnostic to the broader agent-native protocol stack (MCP, A2A, ANP, x402, ERC-8004), independent development teams reproduce the same structural pattern -- confirming the governance gap is a feature of market-driven development, not ecosystem immaturity. Institutional design is most effective before social patterns calcify; we conclude with a prioritized roadmap for the missing governance infrastructure.