The use of "unworthy" does become a stumbling block. Other words, biblical and otherwise, exist. "Fear of God" is a hindrance to many as well. Should we just use different words now that so many hear them as curses rather than blessings, as nullifying, rather than amplifying, our access to God grace in Jesus?
For me the answer is yes, especially if by the words we automatically do more harm than good. This is much easier to do if your theology embraces our being created in God's image to love and be loved. And that the object of following Jesus is not to diminish us but to restore our true humanity.
Being told that we are worthless? It's worthless. Of course the essence of grace is that it comes unearned and with no entitlement. When it comes to grace, God always makes the first move. But God initiates covenant love because we are worth redeeming, created in God's image.