How often do you actually need to handle those errors differently? In my experience, it is vastly more likely that a function which can throw errors in Java looks like this:

  Stuff foo() throws SameException {
    return doOtherStuff(doStuff())
  }

Whereas in Go the exact same function must be written like this:

  func foo() (Stuff, SameException) {
    thing1, err := doStuff()
    if err != nil {
        return err
    }

    thing2, err := doOtherStuff(thing1)
    if err != nil {
        return err
    }
  }

Propagating is by far the most common "error handling" and Go constantly makes you break the flow of the code to do it.