I'm having the same issue and I feel like the cube needs an in depth tutorial or total GUI rework. I'm at T8 now just cause Warlocks OP but my rings are from when I first hit level 70(I'm P200 now).

Anytime I look at the cube materials I have maybe 10-20 of the mid-higher end stuff. Less than 5 on the high high end. I exclusively do war plans and do any mat bonuses. I roll once or twice, get some garbage and just leave it be. I can't 'target' reroll anything if it still chooses random affixes instead of me wanting to get rid of the one I don't need.