The works themselves prove nothing.
I agree. But a lack of works does.
One view of the place of works in the Christian life is given in a very central hymn of the Lutheran faith called "Salvation Unto Us Has Come". Here is the relevant passage:
"Faith clings to Jesus' Cross alone and rests in him unceasing; and by its fruits true faith is known with love and hope increasing. For faith alone can justify; works serve our neighbor and supply the proof that faith is living."
Classic Lutheran hymns are very carefully written because they have a strong didactic purpose. They tend to be "rich" in doctrine. In the verse above, the word "justify" means "save". I'm not sure all denominations use the term, but Lutherans do. Anyway, it's clear that works do not save, but they DO provide proof of faith. Also note the earlier statement regarding the "fuits" of faith ("by its fruits true faith is known"), another reference to works.
Certainly denomination may have differing positions on the relationship between faith and works, but this, at least, is the classical Lutheran position stated in one of its most important hymns.