We don’t lose justification because the doctrine is clearly taught in the very same paragraph that we have been considering. Paul says that sinners who believe in Jesus are justified by God’s grace as a gift (Romans 3:24). And it is because of God’s own righteous character that he grants justification to sinners as a gift of grace through faith in Christ. Even if we take the controverted πίστεως᾿Ιησοῦ Χριστοῦ (3:22) to be “the faithfulness of Christ” rather than “faith in Christ”, we do not lose justification by grace alone through faith alone in Christ alone. Paul is clear that God’s action to justify, which is the fruit of his own righteous character, comes by his grace as a gift (3:24a) in Christ Jesus (3:24b) through faith (3:25). It’s right there.
So, in taking “the righteousness of God” to be a description of the divine attribute of righteousness, we haven’t tossed justification by faith out the window. It’s a both/and rather than an either/or. I would even venture to say that a more robust doctrine of justification emerges that is exegetically grounded in God’s eternally consistent righteous character.