It's also hard to massage your invariants into a form that a type checker will accept, since you're now restricted to weird, (usually) non-Turing-complete language.
A good example of this is matrix operations - there are plenty of invariants and contracts to check (e.g. multiplication must be between m x n and n x p matrices), but I don't believe there's yet a particularly convincing Haskell matrix library, in part because the range of relevant mathematical invariants don't cleanly fit into Haskell's type system.
For those cases, checking the invariants at runtime is your escape hatch to utilize the full expressive power of the language.
This particular example can be encoded into the Haskell type system though. For example, there's a tensor library where all operations are (according to the description) checked for the correct dimensions by the type system. It seems to require a lot of type-level magic though, and that may disqualify it for "cleanly".
A good example of this is matrix operations - there are plenty of invariants and contracts to check (e.g. multiplication must be between m x n and n x p matrices), but I don't believe there's yet a particularly convincing Haskell matrix library, in part because the range of relevant mathematical invariants don't cleanly fit into Haskell's type system.
For those cases, checking the invariants at runtime is your escape hatch to utilize the full expressive power of the language.