>> So the Didache was a way to instruct the new Christians (who were generally not always Jewish by background) in the faith - a teaching tool... <<
Actually, it seems to be more written to gentile pastors, instructing them how to lead a flock. That is the best guess for why it was rejected for the bible: the bible is universal and timeless; the Didache was for pastors in a particular age.
What I heard as the reason for the Didache not being incorporated into the Bible was not this not TOTALLY inspired by the Holy Spirit.
I believe that Jesus does refer to the The Two Ways in the Gospel of Matthew, but I would have to research that. Basically, the Didache uses that theme from the Gospel but points out SPECIFIC policies to follow - much like some of the Old Testament books on laws given to Moses (the eating of pork, etc).
The average Christian may not have had access to the teachings.
Some of the Web Links in this article would give much more detail.
And the bottom line is that if Christians go back to the early Church, we can find common ground between Evangelicals, Baptists, Methodists, Orthodox and Roman Catholic. Something we can all agree on but in different ways... I think that was the original point of this web article on the Didache...
God bless!