I understand a covenant to be constituted by specific parties and obligations/promises. Theologically, I believe thinkers have erred in ascribing elements from one covenant to a separate covenant when this is not supported by the narrative. In the context of the dialogue on this website, for example, I have seen hints that some see "be a blessing to the nations" as something Israel was obliged to do under the terms of the Mosaic covenant. I see the old and new covenants to be related through the Abrahamic covenant in this way:

God promised Abraham (1) the land of Canaan, (2) to make his descendants a great nation/numerous, and (3) to bless all nations through Abraham’s seed. I see the Mosaic covenant as fulfilling promises 1-2 and the new covenant as fulfilling promise 3. I see the obligation to bless all nations to rest on God rather than Israel, though I would be receptive to the argument that the church is instrumental in this. Thus I would see both the old and new covenants in "some way" fulfilling the Abrahamic covenant; I am interested in spelling out in what ways God does and does not fulfill his commitments to Abraham through each covenant.

It is possible to describe God’s covenant partners—regardless of which covenant—as "God’s people," "holy," "chosen," etc. This simply means that God and the people in question are in a formal relationship. It does not tell us anything about the purpose or terms of that specific relationship; so I don’t follow your argument from 2 Peter 2:9.

Finally, I see God’s blessing on all nations as being accomplished through evangelism, more than God’s increasing Abraham’s descendants (though I agree that theme is also present in apostolic thinking). Becoming "in Christ" is good, equated with reconciliation with God, freedom, being saved, light, life, etc. as opposed to alienation, darkness, ruled by sin, etc. So, in order for all nations to be blessed, those peoples must not just experience the blessings of Christian neighbors, but themselves be reconciled with God. There are here-and-now elements of this blessing as well as hereafter; but the Christian—as such, and like Christ and God himself—is motivated by love to experience fellowship rather than separation with as many as possible. Even if it is possible to find fellowship with God apart from knowledge of and allegience to Jesus, that idea remains absent from the New Testament. Rather, when God finds people who sincerely seek him and who’s conduct pleases him (such as Cornelius), his response is to bring them into the Christian church through exposure to the narrative.

While I am in sympathy with your critique of evangelism as it is often practiced—manipulatively, pro-forma, based on simplistic theology, etc.—I can’t find any basis to remove it from the foundation of the church’s mission (or to insert it into the objectives of Israel).