The advent of hierarchical power structures in the church would certainly find fulfillment with the explosive growth of the institutional church that began with Constantine's Edict of Milan (313) and Theodosius II's later requirement that one must be a Christian to be a citizen of Rome (380). But power struggles actually were evident much earlier as the early church grappled with a number of disputes during the second and third centuries--usually related to whether those who had "lapsed" during the persecutions could be re-admitted.
The notion that the presence of the bishop was essential to any meeting of the "church" probably originated with Ignatius of Antioch in the late first or early second century, who said that
all are to respect the deacons as Jesus Christ and the bishop as a copy of the Father and the presbyters as the council of God and the band of the apostles. For apart from these no group can be called a church.
Compare this with the "two or three gathered together" of Mt. 18:20. The notion of one person being greater than another belongs to the World system, not to the kingdom of God. The apostles had a great deal of trouble with this (see Mk. 10:35-45 and the many "first will be last and last will be first" passages in the gospels). The foot washing of Jn. 13 is especially revealing, as Jesus puts on the servant role immediately after the text tells us that he had authority over "all things." What does this say to the house church? Simply that the definition of a "leader" is one who leads in suffering and serving love.
Del Birkey says it well in his book The House Church (Scottdale: Herald Press, 1988), 89:
There resides in no one an inherent right to control another in Christ's church. Nowhere in the New Testament are church leaders instructed to exercise authority over the people of God. Any ecclesial authority is always the authority of the whole (Acts15). Ecclesial authority is never prepackaged according to sex or status, nor is it ever given to any one clergy or federation....
Eldership is always a matter of ministering, not administering. The authority of elders is therefore functional-relational rather than positional-institutional.