I think we can go deeper here especially wince we are dealing with earlier documents. And let me re-emphasize that there is agreement between the Didache and what protestants teach.
There will also be differences when it isn't in agreement with the documents of the letters of the Apostles and the 4 Gospels. There was already problems and issues that had to be dealt with such as:
Paul had to deal with those who wanted to re-establish the law instead of faith and grace as noted in Gal 3:1 O foolish Galatians, who hath bewitched you, that ye should not obey the truth, before whose eyes Jesus Christ hath been evidently set forth, crucified among you? 2 This only would I learn of you, Received ye the Spirit by the works of the law, or by the hearing of faith?
Gnosticism was dealt with multiple times as in 1 Tim 6: Avoid the irreverent babble and contradictions of what is falsely called “knowledge,”
Then we have what I see in the Didache where man has the capacity to make a tradition that makes God's word of non-effect as Jesus said,
Matthew 15:6 And honour not his father or his mother, he shall be free. Thus have ye made the commandment of God of none effect by your tradition.
Just because one is a believer doesn't mean we can't make a truth into a tradition. So taking for wikipedia on Didache:
"Fasting is ordered for Wednesdays and Fridays" - Fasting is encouraged! - But there is no basis for this to be a "law". One doesn't "order" a person to fast. Here they took what is a truth "we should fast" - and then made a "tradition" that it must be done on two days. Does God not accept a Monday fast? Are three day fasts now unacceptable? If you miss a Wednesday, are you less of a Christian?
Would I take a sermon and express the differences today? Not at all, as it has been noted, people don't even know of this tradition.
Remember, this was discussed and found it not to be canonical for the obvious reason that I just mentioned.
But here in this forum, as you brought it up, happy to discuss any finer points.