There are multiple ways to do this. The easiest would be simply to put Attack or Spell Power on weapons, which would still leave them segregated by role to some extent (melee would want the AP weapons, ranged casters would want the SP weapons, and hunters would still be the only ones using bows, crossbows and guns). A more complicated but perhaps more compelling system would be to have them switch between AP and Spell Power, so that a holy paladin could use a weapon for healing, then switch over and use said weapon for tanking. Still more complex but perhaps even more interesting would be to have weapons retain int, agi or strength and switch depending on which class was using them as well as each role. If you visit the original post at 7th Tower, he breaks down how it might look using Siege of Orgrimmar as a template. The current breakdown of agility and strength weapons would, in either scheme, now be available to a broader range of players.
It would certainly fit within the paradigm of broader usefulness for gear established by the changes to armor. The question becomes what are the up and downsides to this?