After studying Kant for a short time the manner in which he talks about our faculties had to be read as a myth (story). The process of intuition giving objects that are then understood (a priori) and so delivered in an orderly manner was not meant to be taken literally as a sequence, but has more the character of stories Socrates would defer to that he couldn't justify, such as the doctrine of recollection in the Meno.
This reading made the most sense due to Kant's acknowledgement that all knowledge begins with experience, yet not that all knowledge arises from it. Another way of approaching this is the following: if pure intuition, or concept, wasn't combined already into experience there would be no vantage point from which to discover it, and this means that these things only have there definite sense if they are seen together.
Kant speaks of his interest in making his work sensible to the reader. Would other stories perhaps make it more sensible? Kant will often allow different accounts to light up the same thing (e.g., the formulations of the Categorical Imperative), and so it seems we don't need to tell a new story as if it must oppose the old one: these stories are not to be seen as facts that oppose each other, but as guides for the understanding. Plato, too, seems to have recognized this and seems to make little effort to have the myths he tell be mutually consistent.
Kant provides an opportunity for a different story in the Critique of the Power of Judgment, particularly with regard to the judgment of taste. Rather than a story about the a priori processing of material, we can instead see the object immediately presenced as interesting apart from a concept. This interest draws us into conceptualization that first employs the empirical (objective) understanding. This objective understanding is exactly the basis for an analysis of the form of understanding. There are some interesting benefits of using such a description that fit very well with Kant's philosophy.
One thing we can benefit from is seeing the givenness of the object as clearly preceding the analysis on it. Kant says analysis assumes prior synthesis, and this should not imply that analysis depends upon a literal bringing together of material. We should see this assumption of analysis as the manner in which the activity of analysis guides itself in separating the material, not as a dependency on a speculative processing of material in the subject. This leads to another benefit regarding the understanding of 'subject' in Kant.
Even today there is a temptation to read Kant as another problematic idealist (i.e., Berkeley). Part of Kant's problem is this subject centric narrative he uses. Starting from the object of taste, we have something closer to the thoughts expressed in the refutation of idealism: that the conception of the subject depends on something outside us. However, this narrative doesn't leave the subject as some pure result, rather it would be the 'I' of the 'I think' (objectivity) that is discovered: we have a definite existence apart from explicit empirical determinations, but with the beautiful object we are brought into our first (objective) empirical understanding, and all at once into an understanding of ourselves as thinking objectively. This way of bringing about the thinking can show us another benefit regarding understanding.
For Kant, the categories concern the form of understanding of objects of experience. Nothing particular is thought by the categories alone. Instead the categories describe the basis upon which one can judge additional attributes. The object of taste is exactly that upon which our understanding is first engaged freely (in spontaneity) to determine the object. Having the object given first as that upon which we judge can help us see the categories more clearly for what they are and how we discover them: they are the form of the understanding and we discover them from an analysis of the objects understood objectively in experience. This further avoids the interpretation of categories as existing in the head, and part of a mechanical process on data from senses that produces experience.
Another benefit of our narrative is that it opens up a relation to objects that has more possibilities than passing over to understanding. For example, from this narrative there is room for considering things as equipment in an environment. This is harder to do when the narrative always delivers the thing to you as understood objectively as such and so particularly in the character of the understanding guided by categories employed in theoretical knowledge. This may open a space to understand topics such as equipmentality through Kant, and also to make use of other thinkers to clear this ground as well.
Ultimately Kant did not want us to repeat his work, but hoped that the work he was doing would help build a common ground for attaining to the more important goals he saw for mankind: expansion of our understanding, perpetual peace, enlightenment, the Highest Good, &c. In the Prolegomena, Kant asks for help from future teachers of critique. Kant does not want teachers of his book, but of the science that exists in idea, and which Kant's book of the same name was merely one attempt at working out. We can't hope to help the exposition of critique by merely interpreting and criticizing Kant's narrative, nor can we do it if we must feel alternative narratives can't be given in the spirit of genuine critique. We can continue the worthy project of critique by giving it a clearer exposition, and so more stories from which to develop understand. I hope that I have suggested the value in this as much as I have given an example.