Although Dickens is very much concerned with injustice and reparations to victims, Little Dorrit is at its core a deeply conservative novel – one that does not seek to overthrow the current system but to instead restore it to some bygone ideal. One of the main tenets of this conservatism is the emphasis on personal duty as the main motivator for action. Characters who are able to put aside their own desires and instead follow the dictates of duty tend to be rewarded, while those who cannot see past their own concerns eventually get the short end of the stick.
In a world as oppressive as this one, characters who manage to completely evade responsibility and duty, like Miss Wade and Gowan, are actually impressive and somewhat worthy of admiration.
Invoking duty is the best way to induce a guilt trip and compliance in the novel, and so it's one of the many techniques used by the strong to subdue the weak.