And could Kant be in bad faith when he proposed it, thinking actually about a rule-utilitarianism ?
Rule utilitarianism focuses on the usefulness of the general rules on which an action is based. It says that an action is good if the rule it is based on produces the greatest happiness for the greatest number.
In one sense there is a similarity between the two views, in that categorical imperatives could be the “rules” of rule-utilitarianism. But because of the emphasis on the end result of an action, they differ.