I'm thinking this would help quite a bit early to midlife of an expansion (when the majority of people are still leveling whatever they're interested in leveling); although, you'll get a hilarious consequence I think from it too. In that you'll get more people who use tank/healer to level other jobs with fast queue times but because they didn't really care for those two roles in the first place they're going to make dungeons generally more rocky for everyone lol. If you've a bad tank and healer a lot of dungeons are going to be quite hard to finish properly, but if you've just bad DD then usually you'll be fine (just slow). Speaking the non-enrage content of course, the more casual / not PF-based content, obviously not fine in stuff that has a damage floor that needs to be met.
Not that I'm saying it can't be tried lol, just think it would be funny that it increased the pool of those jobs but made the content more annoying to run XD. I'd still like to see what happens if it's used, maybe from an event SE releases soul scrolls that you can activate to hold exp (instead of it going to your job / into the toilet if at cap), then you can transfer that exp to another job by using it while that job. Give the scroll a timed life, so that it vanishes by the end of the event- just see what it does to the DF. I like that I can share exp in pvp that way already, so it might be just as cool in DF.
Since we're suggesting stuff though I think a cosmetic merit system might be interesting, and then on top of that tank/healers could gain a bit of bonus merit exp. I'd love for it to be stylized if possible, like a sphere/crystarium/license board. Such a system that has general merit unlocks and then job specific, the exp could by split into types (dragoon experience for dragoon specific merit unlocks) but it doesn't have to be. Either way the tanks and healers would be able to unlock general cosmetics easier, and of course their own merits- if you didn't want to increase the length the system lasts they could also use that exp onto other jobs. Just for random examples you might have cosmetic animation changes, like your dark side dark knight spell getting the shadow effect from trailers, the Manderville Limit Break (hammer attack), Manderville run, dragoon hyper jump (mount), special holy breastplate for white mage (heavy armor cosmetic), etc. If you want you can even put some basic features into that, but nothing that will make players not take in a player who doesn't have X unlock. Like you might unlock shortcuts from one area to another, reduce costs for transportation, unlocking npcs in town, donating / investing to traveling merchant that gains larger stack and greater coverage as you go, you could even go as wild as allowing players to invest their experience into developing a hamlet or something (doma reconstruction, but based on experience points than gil).
Besides making exp more valuable for everyone, it would obviously make gaining experience easily and reliably a big pro to being healer / tank, even more so if they get a bonus in the roulette when in need. Like +20% merit exp on completion of duty (will apply to DD too, if they're in need).
Tanks also have to do a number of mechanics and are expected (well, ideally) to do proper damage too, with a higher expectation they know the fight than other jobs (how far to wall to wall pull, where to stand the boss cross phases, what attacks don't show aoe markers but can still be dodged, what you have to interject, etc). In my experience DD is the most relaxing role, with the exception of maybe certain bosses that have very strict tasks that DD have to do (but usually those contents have things for off tank / healer too then- like if it's an enrage timer everyone is expected to deal decent damage so that's not just a DD thing).
Such that I think Tank has the most consistent stress and healers have the highest peak stress (situational stress) but potentially less than tank when things are going well (if everyone is bad, good luck and it might blamed on you for not keeping them all alive even though they're all sleeping in orange without any mitigating cooldowns ever). DD have to do things, their kits being usually more complex, but in terms of stress of the expectation, social stress at least- I dunno I don't think they're that stressful. You can regularly clear normal content without a DD, or DD asleep on the job, not so much if your healer or tank are (unless it's really early content).