WoW tried this.

What is does is create a ping-pong situation where if the Adventurer in Need bonus isn't up, tanks literally don't bother queuing full stop and dps queue are in limbo until the bonus assignment is refreshed. Then suddenly everyone with a tank spec jumps into the queue all at once and tank queues are now 40 minutes. Rinse and repeat.

It also encouraged every dps who's barely tanked in their life or learned their class to say "heck, why not, can't turn that down!" and jump into a dungeon completely unprepared. It made for some messy runs.

The only thing that would legitimatelly encourage more tanks is better community attitude. By all means, kick the guy who's in dps stance on trash while using no cd's or aoe and ignoring the group and hurling abuse if you give friendly pointers... but don't immediately assume the guy who made a single mistake or two but genuinely wants to do his best for the group is a brain dead moron and hurl abuse at him instantly, start pressuring him and pulling half the dungeon. That just results in removing a perfectly decent tank from future queues and adding another dps to the pile.