The only real way to solve DPS queues

[Altena]

DPS queues are long, have always been long, and will continue to be long.

Adding a new Tank or Healer isn't going to incentivise people to play Tank or Healer.. It will just shuffle current Tanks or Healers onto those new classes.

The only true solution to increase demand is to also increase supply.

My suggestion is this (although it is really too late for this to be the case in Stormblood)..

Increase the new 4-man instances to either 5-man or 6-man instances and scale difficulty / mobs accordingly. Of course this would be too big a job to change all of the current dungeons to this setup, so I am suggesting that any "new" dungeons after a certain point be changed to this.
1 Tank, 1 Healer, 3/4 DPS.

Why? Well it's a simple equation of supply and demand.
You have more DPS queueing than you have slots in a duty - that is why queues take a long time. The simple fix to a high demand is a higher supply.

Let's use 24-man raids as an example.. Tank queues are actually quite bad for Dun Scaith (or at least were, I haven't attempted to queue as tank since a week or 2 after patch release). This is because you have more tanks than you have slots - since there are only 3 slots for a whole 24-man raid.

Increasing DPS slots by 1 in levelling and end-game dungeons would reduce DPS queues times by a good amount.