No wonder it looks less than awesome to you. A contract is just a hack. Ideally, it should not exist because the type system already covers the programmer's intent. Languages that have shitty types which cannot express very much must work around the problem with contracts.

Partially agree, but only for a very narrow definition of what is a contract, which again is the problem stated above.

A good contract system may in fact rely on type-safety as part of its implementation, but types do not necessarily cover all aspects of contracts (unless you're referring to the full gamut of theoretical generalisations of things like dependent types, substructural types, constraint logic programming, etc), and are also not necessarily limited to things that only apply at compile-time.

Aren't contracts a feature of the type system? They encode a specific type that differs from the base type by a more complex predicate, like a constraint check in SQL.