That was kind of the point of my definition, actually—it's easier to predict what type of thing is a bird if you think of "bird" as "the clade rooted on all the theropods that fit through a particular evolutionary sieve" rather than a category with certain characteristics. Not all modern birds have those characteristics. But those characteristics are what allowed the prototypal "birds" to survive where other dinosaurs did not. Their descendants went on to adapt in various other ways, but we still consider them all "birds" for reasons of genetic lineage back to those original birds.