While I agree with your general argument, I wonder if you realize that functional dependencies have a strong, general, and elegant mathematical foundation that long predates their use in Haskell? If you want even a brief glimpse, there's s short article at http://en.wikipedia.org/wiki/Functional_dependencies that might give you some ideas. The mathematics of functional dependencies plays an important role in the theory of relational databases.
I don't know what you consider as the mathematical foundations for associated types, nor do I know why you consider that to be either more general or more "mathematical" (whatever that means) but I hope you'll enjoy the material on functional dependencies.
I admit I was being unfair on fundeps in calling them less mathematical. Nonetheless, something about their addition to Haskell grates on my mathematical sensitivities. They feel "bolted on" in a way that associated types don't. Probably this is because of my own bias which leads me to see Haskell as a subset of dependent type theory, and ATs as some kind of sigma type (though I've never tried to make this precise). Barney.