I question if you've ever done 4v4 past gold/plat with this statement, you don't seem understand why the PLD cover nerf was a much needed change.
As for tank damage, some research on common tank burst potency patterns (1 GCD) in 4v4 on the kill target:
Warrior
- Onslaught + Fel Cleave = 2,750 potency (10% if BB)
- Fel Cleave = 2,000 potency (10% if BB)
Paladin
- Requiescat + Holy Spirit = 2,500 potency (more if higher MP)
- Royal Authority + Holy Spirit = 2,250 (more if higher MP)
Bare in mind a Warrior has one stun every 10 or so seconds which is punished if used incorrectly, whilst PLD has stun every 3 seconds or so. The damage values are similar, if not more in favour of the paladin due to their overall utility.
Where are you getting these ideas that PLD needs to do more damage to be on par with the other tanks? I'd love to see your research/data on this to support your statement.