Using kinds to keep track of the concrete representation of a reference to a type (rather than the concrete representation of the type itself) is one of the real gems in GHCs design.
However, one problem with it is that a polymorphic type, such as [] of kind "* -> *", or a function like map of type "forall a b. (a -> b) -> [a] -> [b]" really only works with boxed types. I always wondered how expensive it would be to monomorphize everything at the level of kinds and have what GHC calls levity polymorphism by default.
Languages like Rust and C++ always monomorphize everything and while this does get slow it is still not the exponential blowup that theory suggests. In fact, there is an ML compiler (MLton) which does the same and it is still not too bad. Doing it at the level of reference representation - which is where the generated code actually needs to change - should be much cheaper and definitely a practical default.
The only real problem I see is that you could in principle write code that does "kind polymorphic" recursion, which couldn't be compiled away. But that sounds seriously crazy and I see no reason to allow it in the first place...