Does it matter? Does it matter who wrote Hebrews? It has not mattered thus far. What matters is that the Church has declared it to be Canon.
It most certainly matters. Hebrews, to use your example, was written by Paul. The other books were written by the other Apostles. It was the Apostles who learned directly from Jesus and who Jesus said would be given “remembrance” by the Holy Spirit to write accurately. No other on earth was given that promise.
>>What matters is that the Church has declared it to be Canon.<<
No it isn’t. God may have used the church fathers at one point to get to us what He wanted taught but keep in mind that He has used Satan to bring us teaching as He did with Job. And don’t go getting you panties in a wad, I’m not equating the RCC with Satan I just used and example. The RCC has also including teaching that is not what was brought to the Apostles remembrance to write such as my example of the bodily assumption of Mary. My main point is that the only people who Jesus said would be given “remembrance” by the Holy Spirit were the Apostles. Those would be the writers that I would have reliance on and none other.
Well, the Church did much more than declare Hebrews as part of the New Testament canon. At the Council of Trent, they said this:
Of the New Testament: the four Gospels, according [Page 19] to Matthew, Mark, Luke, and John; the Acts of the Apostles written by Luke the Evangelist; fourteen epistles of Paul the apostle, (one) to the Romans, two to the Corinthians, (one) to the Galatians, to the Ephesians, to the Philippians, to the Colossians, two to the Thessalonians, two to Timothy, (one) to Titus, to Philemon, to the Hebrews; two of Peter the apostle, three of John the apostle, one of the apostle James, one of Jude the apostle, and the Apocalypse of John the apostle. (http://history.hanover.edu/texts/trent/ct04.html