See I agree that most of the New Testament Apocrypha should not be in the Bible, such as the apocryphal gospels, acts, apocalypses etc… However I believe the works known as the Apostolic Fathers should at least be included in the Bible as an appendix, the reason being, many of our doctrines come from them, and also they were written the same time as the majority of the books in the New Testament, actually some of them very well may have been written earlier than say 2 Peter. I feel the church should call these books maybe not as purely canon, but maybe throw it in an appendix to bibles citing their tremendous value to read.
*The Epistle to Diognetus
*The First Epistle of Clement
*The Second Epistle of Clement
*The Didache
*The Epistle of Barnabas
*Seven Epistles of Ignatius
*The Epistle of Polycarp
*The Martyrdom of Polycarp
*The Shepherd of Hermas
The Catechism cites most the writings of the Apostolic Fathers.
The Epistle to Diognetus is cited in CCC 2240, 2271, 2796.
The First Epistle of Clement is cited in CCC 1432, 1577, 861, 1577, 1900.
The Didache is cited in CCC 1696, 2271, 2760, 2767, 1331, 1403.
The Epistle of Barnabas is cited in CCC 1905, 2271.
The Seven Epistles of Ignatius are cited in CCC 498, 1331, 1405, 2837, 1549, 2175, 834, 2473, 132-134, 1010, 2474, 1011, 496, 896, 1369, 30, 1549, 1554, 1593.
The Epistle of Polycarp is cited in CCC 1570.
The Martyrdom of Polycarp is cited in CCC 2474, 957.
The Shepherd of Hermas is cited in CCC 2517, 760.
As you can see, the Church does encourage us to read them. However, I’d like to point out something clarifying about this sentence: you said, “[one] reason being, many of our doctrines come from them.” That’s not quite correct. These documents mention our doctrines because the authors learned them from the Apostles. Our doctrines don’t “come from” the Apostolic Fathers, but from the people they received them from, the Apostles themselves. The Apostolic Fathers were some of the early people who mentioned our doctrines and defended them, but they didn’t “come up with them.” Jesus and the Holy Spirit gave them to the Apostles, who handed them on.
I hope that makes sense, God bless!