Interestingly, I think the theme of utilitarianism that you have highlighted is very closely linked to the theme of the mechanisation of the human soul, that is discussed at length through the action of the novel. One of the key arguments as expressed in this fascinating text is that the initiation of industrialisation is converting people into machines by preventing the natural progression and development of their imagination and emotions. This is modelled most clearly in the characters of Gradgrind and Bounderby. Gradgrind (I love this name for a teacher!) teaches to strict principles, allowing nothing other than facts to enter his classroom. Bounderby likewise is shown to manipulate and consider his workers in the factory as mere objects without emotion. The factory workers and the children of Gradgrind are actually compared and both are shown to lead lives that are emotion-free and very boring and drab.
This mechanisation of the human soul is exacerbated by the philosophy of utilitarianism adopted by Gradgrind. A key cornerstone of his approach is that human nature is treated like a science - it can be assessed, measured and evaluated as if it were something following a strict set or system of rules. One could summarise his educational philosophy by converting his pupils into bits of a machine that obey rules and do their job without question. Throughout the novel, the danger of such an approach is stressed, focussing on the debasing effect on our lives if such a philosophy is adopted wholesale. Louisa is the example of this outcome - she marries someone she doesn't love and in her adulthood goes to her father protesting that know she has fallen in love with someone who is not her husband. She has realised the shortcomings of her upbringing, and is able to persuade her father likewise. Utilitarianism, it is shown, has its definite drawbacks.