so if I need to check compatibility of types I can just walk the class hierarchy and get an answer.

For languages with parametric polymorphism, note that inheritance is kind of like subtyping. Getting subtyping correct in the presence of parametric polymorphism is famously subtle; see http://en.wikipedia.org/wiki/Covariance_and_contravariance_(...

For languages without parametric polymorphism, it's easy to see why inheritance makes things more complicated. In the case of nominal typing, this walking you describe isn't necessary without inheritance -- a value either is or is not in the exact named type it's supposed to be. In the case of structural typing, it suffices to say that inheritance complicates type inference.

Inheritance is actually even more subtle than subtyping even; e.g. consider http://en.wikipedia.org/wiki/Fragile_base_class