First, the term "papa" is a Latin term for "father" and later for pope. In Greek, then, it is a Latin loan word.
As such, it is applied to a bishop before Leo, but not to a bishop of Rome.
Second, Leo is widely considered the first true pope because he is the first to be widely recognized as supreme in his ecclesial authority and because, as this video points out, he consequently claims to be "the heir of St. Peter."
http://www.bing.com/videos/search?
q=yutube+history+papacy+first+pepe+leo&view=detail&mid=605B0236992F9FF24F71605B0236992F9FF24F71&FORM=VIRHence, Leo is often rightly deemed the first Pope:
https://orthodoxwiki.org/Leo_the_Great
So the title of "Pope" was first applied to the Patriarch of Alexandria, and not to the Archbishop of Rome. What exactly does this prove? Plenty of people before Pope St. Leo were saying that the Bishop of Rome has Apostolic Succession from St. Peter, and is therefore his heir. No one ever disputed that the Bishop of Rome derives its Apostolic Succession from St. Peter, in the East or West.
Third, for Paul, apart from the Gospel of Christ's atoning death and resurrection. demonstrable spiritual power is more important than elaborate doctrinal systems:
"I will find out not the talk of these arrogant people [rival leaders] , but their power. For the kingdom of God depends not on talk, but on power (1 Cor 4:19-20)."
You underestimate how mystical and charismatic Paul is in his approach to the truth:
"My speech and my proclamation were not with plausible words of wisdom, but with a demonstration of the Spirit and of power, so that your faith might not rest on human wisdom, but on God's power (1 Cor 2:4-5)."
Yet, we have every evidence that episkopoi (bishops), presbyters and deacons were all ordained by the Church (I've already cited a few chunks of Scripture, but there's a lot more I can provide). St. Paul himself was ordained by the Church to be a missionary (see Acts 13:1-3). Just because a preacher was charismatic in the early Church by no means implies that they appointed themselves as episkopoi (bishops) or presbyters or deacons. If anything, St. Paul was admonishing those who were trying to do just that--trying to set themselves up as leaders in the Church, over and against the ordained presbyters, without being ordained themselves.
Fourth, for Paul, apart from the Gospel of Christ's atoning death and resurrection. demonstrable spiritual power is more important than elaborate doctrinal systems:
"I will find out not the talk of these arrogant people [rival leaders] , but their power. For the kingdom of God depends not on talk, but on power (1 Cor 4:19-20)."
St. Paul absolutely did teach people to adhere to doctrine, and considered this to be very important. He says to Timothy (1 Timothy 4:5-7):
6
In pointing out these things to the brethren, you will be a good servant of Christ Jesus, constantly nourished on the words of the faith and of the sound doctrine which you have been following. 7 But have nothing to do with worldly fables fit only for old women. On the other hand, discipline yourself for the purpose of godliness
And two chapters later he says the following (1 Timothy 6:1-6):
All who are under the yoke as slaves are to regard their own masters as worthy of all honor so that the name of God and our doctrine will not be spoken against. 2 Those who have believers as their masters must not be disrespectful to them because they are brethren, but must serve them all the more, because those who partake of the benefit are believers and beloved.
Teach and preach these principles.
3
If anyone advocates a different doctrine and does not agree with sound words, those of our Lord Jesus Christ, and with the doctrine conforming to godliness, 4 he is conceited and understands nothing; but he has a morbid interest in controversial questions and disputes about words, out of which arise envy, strife, abusive language, evil suspicions, 5 and constant friction between men of depraved mind and deprived of the truth, who suppose that godliness is a means of gain.
In his letter to Titus, Paul says the following (Titus 1:7-9):
For the overseer must be above reproach as God’s steward, not self-willed, not quick-tempered, not addicted to wine, not pugnacious, not fond of sordid gain, 8 but hospitable, loving what is good, sensible, just, devout, self-controlled, 9
holding fast the faithful word which is in accordance with the teaching, so that he will be able both to exhort in sound doctrine and to refute those who contradict.
And in the next chapter:
1 But as for you, speak the things which are fitting for sound doctrine . . .
6 Likewise urge the young men to be sensible; 7 in all things show yourself to be an example of good deeds,
with purity in doctrine, dignified, 8 sound in speech which is beyond reproach, so that the opponent will be put to shame, having nothing bad to say about us.
9
Urge bondslaves to be subject to their own masters in everything, to be well-pleasing, argumentative, 10 not pilfering,
but showing all good faith so that they will adorn the doctrine of God our Savior in every respect.
In 1 Corinthians 15:1-3 we have this:
Now I make known to you, brethren, the gospel which I preached to you, which also you received, in which also you stand, 2 by which also you are saved, if you hold fast the word which I preached to you, unless you believed in vain.
And in 2 Thessalonians 2:15 we have this: So then, brethren, stand firm and hold to the
traditions which you were taught, whether by word
of mouth or by letter from us.
As you can plainly see, St. Paul was most definitely concerned with "doctrinal systems". Belief and faith were very important to St. Paul, and this includes especially believing the correct things.
EDIT: And I should also point out that it wasn't just St. Paul who was concerned about doctrine--both holding to correct doctrine and avoiding false doctrine. 2 John 1:9-10 speaks about the importance of sound teaching, as does Hebrews 13:9; Revelations 2:14-15 criticizes false doctrine, and then Acts 2:42 says how people devoted themselves to the teachings of the Apostles.
In addition, Acts 15 clearly shows that the Church did have a central authority in the form of the Apostles and the clergy coming together in council. Church councils such as these later came to serve as the highest authority in questions of doctrine and dogma in later centuries, and they all have their root in the Council of Jerusalem, here in Acts 15. The Church may have been far-flung, and there was no one church who dominated all the others, but there was indeed a centralized authority and a hierarchy of clergy to maintain order in teaching and authority.