Or would it do more harm than good because there would be no point in getting Heroic raid gear as the unique color sets wouldn't matter?
I could see that being a problem, but everyone gets Heroic transmog sets for free after the content becomes obsolete, so I don't know. Maybe make it to where only Heroic raid armor, and Elite PVP gear could be dyed?
I personally love the dye system in Rift, and can think of a lot of Warcraft armor sets that don't look too cool with their default color, but would look amazing with a dye-job.