That's not really true. Scripture does imply, a single overseer for a local church. Which agrees with the fact that Jesus Christ is the single head of the Universal Church.
1Ti 3:1 πιστος ο λογος ει τις επισκοπης ορεγεται καλου εργου επιθυμει
Faithful is the saying, If a man seeks the office of a bishop, he desires a good work.
This office is "singular" in the Greek. One man - not men, as contrasted with those who would be Deacons or Servants of the church.
The Greek word: επισκοπης is literally translated: "episcopate". However, it comes from a Greek word that means "to watch" or "to go see". Therefore, an "Overseer".
In the letter to Timothy, it is always mentioned in the singular... just one man:
v.1 ".. If a man..." - .."he desires..."
v.2 "The Bishop (Overseer) must be a husband of one wife..."
v.4 "one who rules his house..."
v.5 "But if a man knows not how to rule his house, how shall he take care of the house of God?"
Additionally, these same instructions are given to Titus:
Tit 1:5 For this cause left I thee in Crete, that thou shouldest set in order the things that were wanting, and appoint elders in every city, as I gave thee charge;
Note here - that Titus was to appoint "elders" in every city, not "elders" (plural) to every church but in every city. After this, the instructions are the same as given in 1 Timothy:
Tit 1:7 For the bishop must be blameless, as God's steward; not self-willed, not soon angry, no brawler, no striker, not greedy of filthy lucre;
Tit 1:8 but given to hospitality, a lover of good, sober-minded, just, holy, self-controlled;
Tit 1:9 holding to the faithful word which is according to the teaching, that he may be able both to exhort in the sound doctrine, and to convict the gainsayers.
Nothing you've said here demonstrates that the churches had a single head, or leader, of any given congregation. That place belongs to Christ. You've used a lot of words that don't really prove anything.