In the study of systematic theology what is the motivation behind creating the term "Covenant of Grace"?

Sometimes I'm not clear why a systematic theologian doesn't simply adopt the Biblical term "New Covenant" but using terms like "Covenant of Grace". What is the reasoning behind it? In the [ESV translation](https://www.biblegateway.com/quicksearch/?quicksearch=new+covenant&version=ESV) the term "New Covenant" appears in a variety of contexts: Jer 31:31, Luke 22:20, 1 Cor 11:25, 2 Cor 3:6, Heb 8:8, Heb 8:13, Heb 9:15, Heb 12:24. Doesn't the usage and contexts created by Jeremiah, Jesus, Paul, and author of Hebrews **sufficient** to justify the use of "New Covenant" as a systematic theology category, making the systematic theology more Biblical? If a systematic theology uses the category "Covenant of Grace" how does it integrate the Biblical term "New Covenant" into its theology and how does the theology contrast it with "Covenant of Grace"? ### Preliminary research - Examples systematic theologians using "Covenant of Grace": see [Mr. Bultitude's answer](https://christianity.stackexchange.com/a/37001/10672) to the question "What is the origin of the Covenant of Grace?". Although the answer shows that the origin was in the Calvinistic tradition, the answer does not explicitly explain why the need to organize their theologies around an *additional* but artificial concept "Covenant of Grace". - Clue from [Nathaniel's answer](https://christianity.stackexchange.com/a/54931/10672) to the question "According to Reformed theology, when did the New Covenant start?" since the answer is framed in terms of "Covenant of Grace".