Genes, Wands and Spells - The magical secret sauce of the "Potterverse"
In the Harry Potter Universe, magical ability appears to have a genetic component. It is possible for Muggles, or non-magical humans to create a magical offspring. The nature of that magical ability is not discussed in any great detail but it appears that Muggle-born wizards are not only possible, but often quite powerful as well.
It is also mentioned that wands choose their user, indicating there is an inherent magical ability shaped into the wands upon their creation. Likely a property of the wood, their point of origin and the natural skill of the wand's shaper. It is unlikely they fall from trees as magical implements so their "nature" is probably released by the wizards who create, shape and refine the magical properties of wands.
Since wands would appear to be amplification tools for magical ability, it stands to reason that common wands would resonate magically and as a result would likely respond to different users in different ways and that ultimately a wand would "choose" a user who could best harness its natural propensities.
Now, any user tends to be able to use any wand, but we have seen that a wand will function best if it is:
- chosen with harmony in mind (being chosen by the wand)
- given as a parent might bestow a beloved wand to an offspring
- taken in a martial certamen or magical duel, as in the case of the Elder Wand
- it is possible to even take a wand from another wizard you have
not dueled but that wand appears to be less reliable and undesired
for protracted periods.
A wand is a tool which amplifies magical ability. If magical ability is nascent in all humans, it would be likely a Muggle touching a wand, who possessed recessive magical genes might be able to get an unreliable, and likely dangerous result from a wand. But most likely (and ideally) would get nothing from an un-attuned or unaffiliated wand.
Wizards would use wands, the same way a tool using human would use a hammer, to augment their natural strength and ability to affect the world. Wizards absorb, control, and manipulate magical energy due to a genetic ability, the same way magical animals would. The difference is likely the use of language or other order-amplifying capabilities that spell casting offers.
So it is likely than using a wand, and the use of order-structuring spell casting gives a decided advantage to someone who is using only one of the two methods of magic use.
Dobbie uses magic without spell-casting but evidently it is not powerful enough to affect strong wizards or there would be no house-elves in the first place. We have to assume that spell-casting is the amplification technology that carried humans to the top of the magical food chain, the same way complex language and later writing allowed humans to transmit knowledge to paper, allowing future generations access to previously-discovered knowledge.
This previous knowledge would allow humans to not have to relearn everything their ancestors knew through trial and error. In a magical world, the ability to transfer spell-casting, an amplification technology, directed through magical items which resonate with the caster and further amplified their abilities would give a distinct (and perhaps, unfair) advantage to magic-using humans.
So, the question is can genetically-capable humans (commonly called wizards and witches) use magic without wands? Certainly. It appears to be an ability used by all magical creatures in the "Potterverse."
The advantage of concentrating magical energy using a wand as a focus, the same way a blacksmith might use a hammer to direct force to metal being shaped, would be a decided advantage in the fast-casting and focused-directing of magical energies.
And if two wizards were dueling with wands and one was suddenly without a wand, such as in the case of disarming spells, he is at a disadvantage both in speed and power even if he has access to spells. If both were disarmed, it might be easier to simply fight physically than to try to control magical energies without a focus, since they would have had less practice doing so, and might be less able to effectively control magical energies in their raw, unfocused form. A wizard who practiced, however, might surprise a wizard who in disarming him, suddenly found the disarmed wizard, still able to create magical effects through discipline and practice.
Wands and other foci probably destabilized the "Potterverse" the same way gunpower destabilized civilization on Earth for the same reason. It allowed concentrated power in the hands of a well-trained force. Magical animals using their power to amplify their physical strengths or other physical abilities could not direct magic in a distilled essence, or if they could, without wands, spell-casting was likely slower or less effective, or had other requirements that made it not as good as fast-cast magic using wands.
Unfortunately, if the "Potterverse" has firearms, it is the same reason, Wizards have not conquered the world. Firearms would place even faster weaponry in the hands of a force that did not have to be as well-trained to be effective. The difference is the same as between the longbow and the crossbow. Relatively equally effective in combat, but the difference in training time was significant. Hence the reason, longbows became an anachronism on the battlefield, replaced by crossbows with their short training time and powerful effects on the enemy.