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they individually were perfect in that moment

This, too, is a mere hypothesis. What the scripture itself tells us is:

The Church won't fail (Mt 16:18)
The Apostles will teach the world (Jn 17:18f)
Peter will convert his brethren (Lk 22:32) and the Church will be one (Jn 17:22)
All Scripture is inspired by God and profitable (2 Tim 3:16) together with the Tradition (2 Thess. 2:14)
No scripture can embrace the knowledge of Christ in full (Jn 14:26, Jn 16:13, Jn 21:25)

The Apostles will teach the world (Jn 17:18f)

Joh 17:18 "As You sent Me into the world, I also have sent them into the world. Joh 17:19 "For their sakes I sanctify Myself, that they themselves also may be sanctified in truth. Joh 17:20 "I do not ask on behalf of these alone, but for those also who believe in Me through their word;

Peter will convert his brethren (Lk 22:32)

Brethren refers to the Jews. Paul's mission was to the Gentiles.

Gal 2:8 (for He who effectually worked for Peter in his apostleship to the circumcised effectually worked for me also to the Gentiles),

the Church will be one (Jn 17:22)

No argument, but in my Bible "Church" is spelled "church". And, quite coincidentally, so is it in my Catholic version.

together with the Tradition (2 Thess. 2:14)

2Th 2:15 (2:14) Therefore, brethren, stand fast: and hold the traditions, which you have learned, whether by word or by our epistle.

Paul states we hold fast the traditions through the preaching of the word or the epistle (scripture). We don't learn tradition through men.

Compare:

Col 2:8 Beware lest any man cheat you by philosophy and vain deceit: according to the tradition of men according to the elements of the world and not according to Christ.

No scripture can embrace the knowledge of Christ in full

Joh 20:30 Therefore many other signs Jesus also performed in the presence of the disciples, which are not written in this book;
Joh 20:31 but these have been written so that you may believe that Jesus is the Christ, the Son of God; and that believing you may have life in His name.

I always get nervous when Catholics post references without any scripture.