The only real way to solve DPS queues

[Penthea]

If the problem is that consistent, though, isn't the issue equally likely to be simply that... tanks and healers aren't attractive enough?

Attraction is subjective. For some players it's not that they hate tanking and healing, it's that they enjoy dpsing far more. Others don't want the responsibility of having the well-being of other players constantly on their shoulders.

And then there's the responsibilities. Perhaps if the responsibilities of DPS were equally visible, a bit more of the ostensible tank/healer burden taken up by DPS, then the other roles would be more attractive, at least relatively.

The responsibilities of dps aren't as comparatively burdensome as tanks and healers unless you do ex and savage. As a dps a few mistakes in your rotation will rarely cause issues in normal mode, and it's true in many savage and ex fights as well. However a tank or a healer making one mistake with their class abilities can lead to a wipe in content even before lvl 50.

Also tanks and healers must learn how to fulfil their roles alone given they're the only tank/healer in the majority of pre max lvl content, whereas dps always have another dps with them. If there was three man content with one tank one healer and one dps, then the responsibility of the dps could dramatically rise.

And as for table-top RPGs, just consider any of the DnD style video games you've approached, or any system with ranged or first-strike mechanics; they, not a tank or healer, are the bread and butter of combat.

I mentioned table-top rpgs to point out that classes specialising in damage being popular is because of human behaviour, not a fault of the game. When a game gives the choice of playing support or damage, damage is almost always far more popular. Full damage teams can work in table-top rpgs because the GM can create encounters specifically for the group playing. You don't have that option in mmorpgs.