I want to suggest an idea from an observation that’s been made many times before. Namely, that what the modern center-left now likes to call “classical” and/or “social” Liberalism, is a muddle of two strains of thought in the Enlightenment, that both stand in opposition to Rousseau; but that the latter strain smuggles him back in through the kitchen door. The division in the Enlightenment between Rousseau and Hobbes is so famous it’s practically a cliché at this point.
If you look closely at Mill’s arguments in Utilitarianism, he seems to be making a very strong response to Kant (perhaps against the Groundwork?). Mill accepts the notion of moral duty, just as Kant does. But he insists it derives not from any form of analytic (i.e., Kant’s notion of synthetic a priori) truth. Rather, Mill insists it derives from the apparently universal desire of mankind (individually, in aggregate) to seek its own pleasure.