What if Basic Attack read something like "Hit: [W]+Ability damage and inflict your weapon's default condition UEONT" or something like that. Now 'Ability' would be whatever is the key ability for that weapon, and each weapon could specify some sort of condition/effect that it is associated with by default.
Now, if you were to assume that all powers were scalable using an augment system as we have discussed before in one or two of the threads on MPs IIRC then you'd basically have a complete weapon style built into each weapon. Heck, a character wouldn't really even need to know any powers. This would be nice in the sense that it would allow every character to be reasonably proficient with one, fairly modest but usable, 'style' of fighting. Furthermore, given there may be weapons suitable to at least most ability scores, they'd be actually effective with it.
This would open up some other design space, as it removes the absolute need to have every character have some at-will they can always use. Not that I think wizards should all be falling back to dagger fighting, but its not a BAD thing if you can create a wizard that is actually pretty good in a knife fight if you want!