No. We are indeed not under the Mosaic Covenant today. But the laws, written in the Mosaic covenant, the moral part, the part that is restated by Jesus and Paul, and Peter in the Epistles, is indeed still a standard that we can look to as a way of life.
Now you get it.
NCT does not say ANY of God's moral laws are obsolete.
The only difference here is you view God as restating moral parts of the Mosaic Law where NCT views the Mosaic Law as being established by Christ (by God, His moral law).
And there is a difference in authority. You objected to NCT saying we are not under the Mosaic Law but instead under the Law of Christ. NCT views our obedience to the moral laws as obedience to Christ (if you love Him you will obey His commandments).
Granted, either way one will refrain from sinful actions. But the NCT places the reason we obey in the person of Christ - we are to be holy because He is holy - rather than obedience to a covenant God gave to a specific people at a specific time in the Old Testament.
What does NCT add? Nothing. That is the point. Rather than developing a system of extra-biblical covenants NCT relies on Christ.
Covenant Theology uses "covenants" that are forced into the biblical narrative. The covenant of works is unbiblical and based on a logical fallacy. The covenant of redemption is extra-biblical and tries to establish theology by going around Christ. The covenant of grace is unbiblical and extracts all significance from the covenants that are actually in the Bible.
Whether right or wrong NCT takes its authority from Scripture and it's view literally from what is written in the text of God's Word.
Whether right or wrong Covenant Theology takes its authority from men who were wrestling with Roman Catholicism and imposed a way of viewing Scripture that supported their understanding.
Why criticize NCT, even if you think it incorrect, when Covenant Theology is complete extra-biblical in its framework?