Well, "(erroneously) handled by an intermediate handler" is a tricky situation: would it be really handled incorrectly?
Another question is ergonomics. It's trivial (but tedious) to write code like this:
class Foo {
// ...
public void Frob(...) throws FooException {
try {
// ...
}
catch (Exception e) {
throw new FooException(e);
}
}
public void Blarg(...) throws FooException {
try {
// ...
}
catch (Exception e) {
throw new FooException(e);
}
}
}
which is actually a "best practice" already ("annotate inner exceptions with some high-level context and wrap them in high-level exceptions") — and adhering to it makes your proposition completely extraneous, because nothing can throw an UnknownException ever.
And in before "don't catch and wrap Exception!", consider that Foo maybe parameterized by some dependency that may be implemented as a network service, or a disk file, or a DB: three different implementations will throw completely different exceptions: FileNotFound vs NetworkConnectionClosed vs OdbcInvalidManufaturer. Either dependency interface allows implementations to throw any of those (so that the user of Foo, who knows which implementation it specified, can handle those), or it makes them to wrap them all into DepException, but then, again, this means that Foo's methods will catch-wrap-rethrow DepExceptions instead of just Exceptions.