The construction of arbitrary convolutions of logic is not demonstrative of your assertions. A multitude of code paths is not specific to checked exceptions. Note: It is possible to try catch a union of exception types in the recent versions of Java (catch X | Y | Z).

The paths are still there if the exceptions are all unchecked or combined or not using exceptions at all. Passing exceptions up is rarely the right choice, imo. If it's a terminal runtime, sure, obv.