Right now we have rewards in the form of loot boxes to encourage people to play roles with lower queue depth. I suggest another incentive.
What if (in addition to, not instead of) the current rewards, winning 5 games for any role that has a reward would prioritize you in the queue for 2 games on any role without a reward.
For example, you play and win 5 games as a tank (they don’t even have to be consecutive), then your next 2 DPS queues would be shorter.
You could even implement a similar UI to the one in arcade and scale the reward the same way. There’s lots of ways to implement it, but conceptually the idea is that you can improve your queue time by spending some time on a different role which would reduce everyone’s queue time if enough people took up the offer.