It doesn't. Not really. We've seen that in multiple games, and here when HW came out. Once the initial shiny new period wears off, people go back to their preferred roles. Adding new tank/healer jobs appeals a lot to people who already play tanks/healers. It does little to nothing to entice people who don't want to do those roles. YoshiP talked about that before, where the overwhelming majority of DRK players were playing tanks before that, and the overwhelming majority of AST players were playing healers before that.
We've seen the same thing in reverse in Stormblood. Outside of the initial new and shiny period, queue times have largely gone back to where they were before SAM & RDM were introduced, and the old order has reasserted itself. Once queue times hit a certain length and the initial shiny period wears off, people largely migrate back to their preferred roles, with the tank & healer players encouraged to do so by not having to wait forever to do anything.
Doing something drastic like increasing group size to 5 would help because you'd get 50% more DPS through the queue for every tank and healer, but that is a HUGE undertaking, to put it kindly. That's the kind of thing you have to decide pretty early on in development and it becomes a nightmare to change it later.
(It's a good thing I like healing and don't hate tanking, because with the play time I have, I'd probably quit if I had to sit in the DPS queue constantly as spending half my time waiting just isn't very fun.)