I feel like this feature could be implemented on top of more universal features.

Checking input parameters is easy, just write asserts at the start of the function.

Checking result requires "destructor" block and some kind of accessible result variable, so you can write asserts in this destructor block which you can place at the start of the function, as well.

Checking class invariants requires a way to specify that some function should be called at the end of every public function. I think, it's called aspect-oriented programming in Java and it's actually useful for more things, than just invariant checking. Declarative transaction management, logging.

There are probably two schools of programming language designs. Some put a lot of features into language and other trying to put a minimal number of features into language which are enough to express other features.

Having the higher level abstraction built into the language gives extra semantic meaning that can be taken advantage of to build tooling. For example, one could build a symbolic model checker based on the contract specifications. It would be possible to do the same with the lower level features, but a lot harder if they aren't used consistently and correctly.

Same reason function calls are better than arbitrary jumps.