Morals have to move us. This is the is-ought distinction. We cannot purely reason our way into our morality from what is, we have to be driven by a feeling of how we ought to behave, how we want to live, what kind of person we want to be in life.
Shame and disgust are physiological reactionions grounded in our biology and evolutionary history, which can be highjacked and repurposed to also serve social aims. For instance we conduct sexual activity almost uniquely among animals, overwhelmingly in private; and this is known to help support cooperation. We feel intuitions, values, judgements, then we reason our way into justifying them. We can understand that a generalised sense of justice, based on intersubjectivity which is to say treating others as like ourselves, supports wider cooperation than a morality about family or clan in-group preferences. So we see groups that switch to more intersubjective moral reasoning being more succesful, for instance by supporting trade networks with a wider range of peoples and cultures, and by sharing technological and social innovations across a wider community of innovators.
So, in a sense our choices of moral theory is about feelings in response to them, it is an aesthetic choice - albeit with practical consequences. Elegance, beauty, or sublimeness, might impact who we want to listen too, who's ideas we are drawn to read. But they are not enough on their own.
Kant's picture is very appealing if the paradigm for understanding you hold highest s mathematics; the axiom of the Categorical Imperative allows many reasonable seeming inference to be drawn from one idea. Utilitarianism picks a quantity to maximise, comparable to a paradigm from physics, like the principle of least action, or increase of entropy in thermodynamics. But, ask a Kantian how they feel about lying to a murderer at the door to save a life (On a Supposed Right to Tell Lies from Benevolent Motives). Ask a Utilitarian if all pleasure is equal (the Utility Monster), or see how they feel about Peter Singer's provocations about the special status we grant to human bodies (Wikipedia section of his utilitarianist views on Euthanasia and infanticide).
We can make elegant, beautiful, sublime moral theories. But if they don't compel people to act in alignment with the force of their arguments, they have failed. And fundamentally, that means they have to help the community that holds them to prosper. There are incompatible moral communities around the world, and the only true backstop we have in choosing between them, is who's lives are flourishing most. To which aesthetics matter, but economics can give a hell of a lot more choices about. I guess you could compare it to Maslow's Hierachy of Needs, aesthetics are there, as a final criteria, but only if the stack of other needs to help us live well together are met first.