I don’t think there is much that can be done to make tanking or healing a more attractive role for players not already doing it.
WoW is a mature game at this stage in its lifecycle, and there are well-established cultural norms regarding how players are expected to play and conduct themselves in group content. Those are, generally speaking:
- Knowing your role and your spec - group content is not considered an appropriate place to learn the core of your spec
- Knowing routes and key mechanics in dungeons - particularly if you are the tank
- Knowing how much is appropriate to pull to complete the content at an optimal cadence without causing wipes - nobody wants to go slow
While these norms of group play in WoW are sometimes bemoaned by, or on behalf of, newer players trying to get into the game, it is understandable where they have come from. A lot of the player base have been playing the game for a long time, some playing it almost exclusively, and thus have an exceptional level of knowledge about the game - including what an acceptable level of play looks like for each role.
These norms represent the largest barrier for someone to get into tanking or healing. DPS rotations can be practiced until they are muscle memory on a training dummy. While there is more to learn, having your rotation nailed gets you a lot of the way there in taking part in endgame group content without being a burden. Tanking and Healing are, by comparison, a more reactive type of play that cannot really be learned outside of actually engaging in that content.
So learning to heal and tank really requires that players throw themselves into it and learn by doing, which can be an unpleasant experience for both the player learning and the group that just want another clear.
The best case scenario is to make a group with friends or guildies who will be patient with mistakes, as opposed to PUGs who will be much more minded towards clearing the content in good timing.
One thing that might help with that is to have some sort of instanced area that the player can go to, which would allow them to spawn in mobs and bosses from the Dungeons for that season, in order to get a sense of their damage output at different key levels. Having a sense of that might go someway to helping newer tanks get an accurate picture of how many mobs they can grab at once, perhaps.
A last point to consider is that no matter what incentives Blizzard creates for Tanking and Healing, it might only be a small minority to genuinely find playing those roles to be fun. I know that I personally do not find either role fun, and no incentive would have me play them. As pointed out elsewhere in this thread, Tanks and Healers already have the incentive of being in high demand, and being able to pick and choose their own groups, compared to DPS where the supply outstrips demand.