Checked exceptions failed in Java because they don't play well with parametric polymorphism. Union types might help (exception list declaration is actually a union type) but I don't think it would succeed anyway as it is not general enough.

Handling effects and effect polymorphism in programming languages is an active area of research and there are some new languages that try to approach the problem (ie. Koka).

Haskell has several effect libraries (effectful, cleff, eff, polysemy) that look quite nice.

Idris with its dependent types allows precise definition of effects in function signatures.