Practical type inference for Hindley-Milner-style languages with higher kinds is not a problem, see e.g. [1]. The problem is adding sub-typing.
I'm also not 100% sure it's correct to say that ML-style languages have no problem with type-inference. I'm sure Robin Milner would have preferred having full, unrestricted parametric polymorphism (i.e. System F) in ML. Alas System F has undecidable type inference [2]. Hindley-Milner is a restriction of full parametric polymorphism that enjoys type inference, and is expressive enough to type many programs. BC Pierce says that the Hindley-Milner "has hit a sweetspot". I concur.
[1] M. P. Jones, A system of constructor classes: overloading and implicit higher-order polymorphism. http://www.cs.tufts.edu/comp/150GIT/archive/mark-jones/fpca9...
[2] J. B. Wells, Typability and type checking in System F are equivalent and undecidable. http://www.macs.hw.ac.uk/~jbw/papers/f-undecidable-APAL.ps.g...