Honestly this would probably just reduce the amount of healers and tanks since... Well now I'd be forced to queue up as dps to maximize my tomes. Currently I only queue as a healer or tank anymore.

It has been shown time and again using a carrot on a stick method to get players to play classes they don't want to doesn't work. The greatest benefit is already there in terms of having a shorter queue and still the ratio is off. The only real way to alleviate it is to adjust party compositions such that the ratios of the roles in the party better match the overall community's desired role breakdowns. But rebalancing content to increase dps role slots seems like it isn't worth it. The only truly terrible queue time now are caused by the ninja influx which will even out eventually.