I believe it's at least possible to modify the master WikiProjects template on enwiki so that we can supply the PageAssessments parser function the file names of the icons for each assessment class. This would mean consumers of the API wouldn't need to hardcode the class/icon relationship. This feature should of course be optional, as some projects may have a conflicting process, perhaps without any standardized icons.
Adding such data via the parser function isn't ideal, as it basically means you're submitting the same data to the parser millions of times in order to just record it once. Maybe some kind of class management interface would be better. Also, I'm not sure how much we should mix data and presentation, at least in the API. Might require some more thought on the use cases.