Okay, I'm anaswering generally, because you said, "Is this really just a phenomenon in Flex/AS3?".
In your init method, obviously you're always calling addChild with foo. That means foo must always be an instance of DisplayObject. You also want it to be an instance of IFooable (though it's not clear here why). Since DisplayObject is a class, you would consider using a subclass of DisplayObject (e.g. FooableDisplayObject), that implemented IFooable. In Java, this would the below. I'm not familiar with AS, but I think this shows there's not any general flaw in interfaces here.
interface IFooable
{
public void runFoo();
}
class DisplayObject
{
}
abstract class FooableDisplayObject extends DisplayObject implements IFooable
{
}
class Foo extends FooableDisplayObject
{
public void runFoo()
{
}
}
public void init()
{
FooableDisplayObject foo = new Foo();
foo.percentHeight = 100;
addChild(foo);
}