The claim that there is no poet morally nobler than John Webster is impossible to prove, for that would require the person making the claim to analyze the morality of every other poet and then show that Webster surpasses them. However, it is legitimate to claim that Webster writes with a strong moral sense and commitment, and we can illustrate that by looking at The Duchess of Malfi.
In the play, the widowed Duchess falls in love with her steward, Antonio. She could have carried on an affair with him, perhaps, for he is certainly of a lower class. But she does not. She chooses to marry him instead, even knowing that her brothers will be furious (for they want control of her wealth and title). Further, the Duchess hides Antonio to protect him, even though this means that people will think less of her, for it appears that she is having children out of wedlock. She puts her husband before herself. This shows a strong moral character.
The Duke, on the other hand, is a morally abhorrent character who is bent on doing whatever he must to identify his sister's new husband. His agent, Bosola, acts as informer, and the Duke vows to ruin his sister completely. The Duchess refuses to give in to her brother's demands even when he threatens her and turns violent. She plans Antonio's escape with the aid of another faithful servant.
But in the end, the Duchess, two of her children, and Antonio are betrayed and killed. The Duke, however, literally goes crazy because of his action, and he and Bosola kill each other. They get what they have coming for their violent, dishonest, greedy, and immoral actions. The surviving son of the Duchess and Antonio steps into his mother's ruling position at the end of the play, which is as it should be.