You miss the point entirely. The Church is a complete longitudinal study in network versus hierarchy. Network prevailed in the first phase. It captured and only then imitated Roman hierarchy. Then the secular hierarchy collapsed and the Church necessarily returned to network mode, building the great monastic institutions that preserved learning through the Dark Ages, and formed the great correspondent Universities to pass on that knowledge.
Then as the Germans imitated the Roman hierarchies to create Feudal hierarchy under the non-Holy, non-Roman, non-Empire, the Church followed suit. Then result of this competition for preeminence contributed to the schism with the Greeks.
Then as the nation states began to imitiate the imperial hierachies in miniature, the Church did continued its competition for hierarchy. That competition with the rise of nation states contributed to failure of the near healing of the Greek schism at the Second Council of Lyon in 1274. The Protestant criticism that then arose in the increasingly nationalized churches was not entirely wrong, as the Counter-Reformation acknowledged. The Counter- Reformation is only now nearing a sense of completion in the rapprochement among many Protestant lineages and the essential end of the schism with the Greek and Eastern Churches.
Aikido needs to take a page from the Dark Age and medieval pattern of networked repositories of learning, which saved and spread much that would otherwise have been lost. Much hierarchy around the world is teetering into chaos. You can look to the Yamabushi, if you prefer, or the Buddhist experience with hierarchy over network, but the pattern has relevance across cultures. India has almost no Buddhists because Buddhism wedded itself there to the Ashokan state and it did not long survive their mutual collapse, but thrived at and beyond the fringes of India. The collapse into rival national states until the Mongols came, mirrors the European middle ages and renaissance.