Could always offer higher rewards, mats, honing buff, etc (that only apply to support classes) to incentivize players to bring up their supports. Seems like the most wise way to go about it, otherwise there will always be a large shortage.
uhhh no
Even with that incentive most people would likely just relegate it to an easy lopang alt or chaos dungeon alt. The core problem is support at progression level. And doing a ‘bonus’ all the way to current content would be very very overkill