Why should a Christian read a significant portion of the apocryphal literature?
Because falsehood and deception breeds on ignorance. The Truth does not fear the unknown, or anything at all; rather, it exposes darkness for what it is. Do not found your faith on ignorance. Have you found God’s Word to be true in view of every other option?
When every other alternative is surveyed and found out, it is seen that there are no competitors to God’s Word, no part of God’s Word has been lost, and necessarily, no other book will ever be added to the Canon of the inspired Word of God.
Here is a large collection of resources on the Apocrypha and Pseudepigraphia, demonstrating that the apocryphal books are not the Word of God, with an Introduction.
And yet, nonetheless, many reformed theologians from the Reformation and puritan eras thought that the Apocrypha had some value both historically speaking and for religious edification (just as other religious books may have today).
Here is the start of a collection of commentaries on the Apocrypha, including from historic, reformed theologians (mainly in Latin):