This is interesting, but it does disconnect the Gospels from the rest of Scripture fundamentally by denying the validity of the epistles and how the epistle use the Old Testament text. A lot of things happened in Jesus' death, but one of the things that did happen was Him dying for our sins as an atonement and freeing us from death [see Romans 5, 1 Corinthians 15, and Hebrews 2]. It's okay to say that Jesus death functioned as a salvation for the Jewish people to save Jerusalem from itself [despite the problems that come from considering how Jerusalem was destroyed 40 years later and the Jewish people crushed], but why does there have to be a denial of the clear historic Christian claim of Jesus' death as an atonement and freeing us from death.

Second, you're right to say that a simple profession itself is not what saves us, but rather a radical transformation of our hearts by grace. However, there is a clear tie between the profession of faith and salvation itself. Littered through Acts are various statements of "believe in the Lord Jesus Christ and you will be saved".

Third, C. S. Lewis' [and Karl Rahner, etc.] doctrine of "anonymous Christians" are definitely interesting, but they don't extend as far as you would hope. Even under those paradigms, it's very limited in what it allows -- those who are unintentionally aligned with a Christian ethic who haven't rejected Christ and the Church [as Rahner puts it]. This doesn't diminish the need for an explicit need for Jesus for those who hear of the gospel. If someone hears of Christ and rejects Him, then they are not saved under this stream of thought.