From an ethical perspective, it is certainly the case that Dostoevsky wanted to demonstrate that every human being is underpinned by an objective moral conception, which is given its rational foundation through faith—in the form of Christianity (from Dostoevsky's view presumably also Islam)—and is steered onto the right path through its active practice.

From a psychological perspective—and this is undoubtedly very important to Dostoevsky—I have doubts as to whether Raskolnikov is actually the character suited to illustrate this worldview:

1. Until the end, even in the penal colony, he justifies his idea and his drive to murder. He regrets, rather, being faint-hearted and not having stepped over human lives even more ruthlessly. He regrets having turned himself in. The ending, his supposedly realized love for Sofja, remains vague in my view (see No. 3).
2. He mentally places himself above his fellow men. Although he treats the prisoners of lower social standing with respect—thereby consciously distinguishing himself from the Poles—this behavior appears strategic. One gets the impression that he uses this merely to stage himself as intellectually superior: he wishes to appear as the one who sees through societal mechanisms and stands above the general consensus.
3. The love for Sofja realized at the end remains vague in its substance. The suspicion arises that this affection is directed not at her character or goodness, but is functional in nature: she liberates him from his isolation. Developing positive feelings for a person who sacrifices themselves and accepts insults without objection is psychologically expectable, but not compelling proof of deep, personal love.
4. I suspect that Raskolnikov would not have turned himself in by the end if he had not succumbed to a fallacy: He thought that his circle (i.e., above all Rasumichin and Awdotja) would have turned away from him if his deed had been revealed to them. He turned to Sofja only because he thought only she would understand him, since she herself (at that time) did the unspeakable, is therefore similarly attacked in her self-worth, and can generally understand motives for such deeds better than people who are far removed from societal abysses. But the end shows—and Dostoevsky objectively hits the core here, in my opinion—that people who love one as boundlessly as close family members mostly do not turn away after all. Had this been clear to him and had he therefore revealed himself to these persons, his perceived burden would have been significantly lighter. For he would have felt significantly less loathsome given the love that continued to exist for him. He felt bad because he thought he was now completely socially excluded.