Most places where exceptions are thrown do not want to handle the case of resumption. Being usefully-resumable requires careful design at the site where the exception occurs, it isn’t something you can just throw in (no pun intended) as a general feature of all exceptions.

From an interface-contract point of view, exceptions model the case that an operation cannot complete normally. Any mechanism that enables an operation to complete normally after all upon encountering an error condition, should better be modeled with a separate language feature, for example with callbacks specific to the concrete error condition.