An at-will power is anything that you can do at-will. These have existed in every edition. Same with daily powers. Encounter powers are the only novelty of 4E, and I believe they were introduced in 3E.
4E just gave those powers a name. Just like Napoleon Complexes existed before Napoleon.
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Warrior Melee Full Attack
You steady yourself, then lash out with a flurry of deadly blows.
At-Will * Weapon
Standard Action Melee weapon
Target: One creature
Attack: Strength vs. AC
Requirement: You must not have moved during this turn, except to shift up to one square.
Hit: 1[W]+Strength modifier damage
Level 6: Make a second attack against the same or a different target. This attack has a -5 penalty to hit.
Level 11: Make a third attack against the same or a different target. This attack has a -10 penalty to hit.
Level 16: Make a fourth attack against the same or a different target. This attack has a -15 penalty to hit.
Special: After using this power, you are unable to use actions to move, except to shift up to one square, until the end of your turn. If you have already shifted this turn, you cannot shift again until the end of your turn.
An at-will power is an action you can take at will. Every action you can take at will is not an at-will power however.
Defining something as a power brings a lot of baggage with it. In your example you include a "warrior" tag for some reason, even though in 3e iterative attacks are not restricted by class types, merely BAB. Likewise you were forced to use a kludge to mimic a full attack being a full round action, although as written it will still permit you to move and then full attack but not the reverse. Awkward.
In 3e on the otherhand, it fit neatly into the action economy, and was not specific to any class, race, weapon or role. It was a standard action type. In 4e you had the Basic Attacks on page 287. On page 289 however I'll note that you have 11 actions which are specified by action type in the combat system but not described in the text. Administer a potion, Equip or stow a shield, Draw or sheath a weapon, Drink a potion, Drop prone, Load a crossbow, Open or close a door, Pick up an item, retrieve or stow an item, drop held items, talk. None of these are defined in 4e power lingo. Neither is breathing, spitting, doing up your fly, getting dressed or daydreaming about your childhood sweetheart.
Does that mean these things are not at-will powers? Or does it mean that some things are perfectly fine existing outside the rigid framework of the AEDU system?
And AEDU is hardly the only way to manage power economies. For example every previous edition of D&D included variable or static recharge rates on some powers with dragons breath being the classic example, but binder 5 round cooldown powers or Bo9s style maneuvers also qualifying.
Other approaches include diminshing returns (truenamer), power points, inventory, power pool (Incarnum) and even stretching a resource allocation across an entire level (artificers.)
4e does not encompass the length and breadth of everything D&D has ever been or done, nor does everything fit neatly into it's slots. The basic attack does actually fit pretty neatly into the 4e framework, as well it should. But even something as simple as the 3e full attack shows that action systems can cover more ground than 4e does. AD&D style mutli-round casting times for example don't work well in 4e, and would actually be a disaster to attempt in such a high-mobiltiy tactical system.
Each iteration of D&D has its own strengths, and should be examined for it own merits when valuating applicability for 5e, rather than insisting on viewing everything through the lens of your favorite system, whether that's a 4e fan claiming everything is a power, or a 3e fan claiming every class in 4e is a caster.