From these given facts, a certain pattern emerges on examination. All creatures cited accord to this pattern. Study or examination of living birds including pre-passerines reveals behavioral aspects that reinforce this pattern as a thesis. This thesis is presented below in the form of an anatomical checklist, that determines whether a given creature is a bird and can be called such in full and without mistake:
Has anatomical feature # 1 .... and has all the others too (barring marginal species, which may lack any one anatomical feature of #s 2 through 7, - but lack one of these only or, by rigidly mechanical judgement according to these rules, they are not birds.)
Argument: A beak is what makes a bird, not feathers at all! Microraptor had feathers but is otherwise not birdlike aside from being obviously made for gliding through the air; Archaeopteryx had feathers and something like wings - but two exceptions to the anatomical checklist, to wit a considerable/heavy tail & no beak - jaw structure was fairly heavy and definitely toothed. Other small 'dinosaurs' may well have been feathered, but lack other anatomically birdlike features.
Hesperornis had teeth, but not robust nor in sockets, and its mandibles obviously formed a beak; this makes it a true bird though the most primitive known; If fossil remains of this species are be found with skin impressions preserved (or of a carcass mummified before fossilization),
it might conceivably not have feathers, but blubber beneath the skin (to insulate it, as an unquestionably aquatic species, in the manner of a pinniped seal or cetacean whale), or even scaled skin for all anyone knows....
[For all I know, such a fossil has been already found at date of writing... though I would most likely have heard of it, it is not impossible!]
As well as a beak and feathers, birds are characterised by their neck: it has many joints and is thus flexible as a snake or even more so. Thus owls can turn their heads 'all the way around'; most birds preen all their feathers with the beak (except head feathers, which are groomed with the feet) because their dexterous neck lets their beak reach, by twisting and turning and reaching, to any feather below mid-neck; birds build nests using the beak as a grasping instrument for the materials, but the flexible reach of the neck allows exact positioning of the nesting material in almost any orientation.
Herons, according to this new view, are the most typical of birds: their beak, acting with the flexible/extensible neck, allows them to strike at and catch fish from a distance. And flight with (feathered) wings allows herons to go to hunt in a great many places, rather than only one or a few.
Having a beak also affects birds' eating: The beak being toothless, they do not chew food but swallow it (or large pieces of it) whole, the food being in many birds rendered by the grinding action of gizzard stones.
And having a beak-and-neck combination means, Birds are pecking creatures: Typically they can, and do, strike at things using the beak as a knife or club, it being propelled by the muscular straightening of the sinuous neck.
One great issue that determines 'What constitutes a bird?' is, the question of the ratites, a more primitive group of living birds, all of which are flightless. Ratites lack the keeled breastbone, which evolved to provide a large area for attachment of the muscles needed for wingbeats; and so of course they have reduced wings or even (in the kiwi) none, since the wings are not needed for flying, and the beak-and-neck combination serves for all purposes (grasping things or moving things) that forelimbs are used for in many non-birds.
Ratites being non-flying, and not keel-breastboned, but nonetheless birds beyond question, means that 'birds' in general does NOT mean 'flying creature' nor 'winged'. A general definition that covers the ratites must eliminate those two descriptors.
An interesting question is, whether the ancestors of the current ratite birds ever flew at all; the lack of a keeled breastbone would seem to indicate that as possible if not probable. -Did flying evolve after feathers, in the ancestors of birds? Supposing that no ratite ancestor ever evolved the anatomy of flying, that would indicate that the common ancestor of both groups of birds (ratite and non-ratite) was not so much 'winged' as 'beaked and flexy-necked and feathered'.
- In which case, what bird needs Archaeopteryx as an ancestor?
If a proto-ratite was the ur-bird, that would indicate that beaks and the associated flexing/snakelike neck evolved first, and implied anatomical weight-reduction, incidentally the first evolutionary step needed for the development of flying ability.
All modern birds show signs of such reduction all over their anatomy: the beak lacks teeth, the feet and lower legs are bony and (usually) featherless and rather fleshless, the entire bony tail structure is reduced to almost nothing, brains and heads are not large, and in many cases structural bones are hollow. Weight-reduction can be seen as necessary for the beak-and-neck combination to be effective: for a beak to strike rapidly, it cannot be slowed by a large head or heavy brain; if it is effective, no multi-digited forelimbs are needed for grasping, so forelimbs rudiment in the direction of wings (or down to almost nothing); feet needn't be weapons and don't have to support as much weight, so they also tend to become more fragile.
A creature of this sort being warm-blooded, it needs insulation over its body surface, and thus was feathered (by sheer chance at first - but think: how could wing pinion feathers and tail feathers have evolved from hair? any creature that could fly had to either have stretched skin dependent on bones (as bats/chiroptera, and pterodactyls among the dinosaurs), or... feathers.)
A nearly impossible fantasy - "Birds with hands":
The Hoatzin bird, as a chick, has finger-claws on its wings. Modern genetics (from what I understand) says that this is owing to the genes for fingers not having been lost, just deactivated, to cause the rudimenting down to a fingerless unbranched limb that constitutes a bird's wing. Being deactivated, they can reappear in the juvenile Hoatzin by reactivation. (?)
If this is so, someday a bird (presumably flightless but not necessarily ratite) may have hands again. Of what usefulness would that be? Only, perhaps, for the multiple-grasp holding of objects in the way of tools, or perhaps to aid the rending or rendering of food. If either of those, then A) the creature would be somewhat intelligent, more so than a monkey if not as much as a man, and B) it might reduce the length/number of its neck bones, and not peck at things as much.
Such a fantastical creature would be feathered and beaked, but not really a bird any longer. It would merely be descended from a bird.