Damage dealers in all games with clearly defined roles suffer from the same problem. Technically they are the easiest classes to play and the most "rewarding". It just feels rewarding to drill the HP of the mobs into dust with your own work. As a result, majority of the players are drawn to DPS. What's worse, in Stormblood, two particularly cool and highly requested classes were added...as DPS. Result?! People that were often/strictly tanking or healing were drawn to those cool, requested classes and are clogging it up even more, doubly so for both increase in DPS population AND decrease in tank/healer population.

However, that is not the fault of the game and as such it cannot be solved mechanically. The only means to ease it is to make other options that either can be done solo or that can be done successfully with only DPS, so that the queues would be strictly based on whether someone else queues up or not. Not what class they belong to. If they will give viable experience, they will be used instead. Everything else is counterproductive and will result in worsening the situation, because it will either make DPS even MORE rewarding for players to play, or make tanks/healers less so.