Give tanks some form of reward that doesn't suck. Like a gil amplifier during dungeon (Make it silly, like 5x more gil) and everyone and their mom will queue as a tank to generate fresh gil, they can then throw at the economy.
It would upset the economy for a while, until it stabilizes. Worth the trouble IMO.

Other than that, you'd have to make every class/job viable as a tank/healer in some way (Via traits/subjob abilities, etc). Which could take a while, but IMO might be the better/more fun way to go.
Sadly, everyone would whine/complain more so about this than the above. Additionally, Yoshi's vision is dating back to 2004, so I doubt he'd even consider it.