You do realize that your explanation suggests being much more reliant upon the healers, rather than it being a result of the Warriors cooldown capabilities, right?
To even suggest Warrior and Paladin are equal in anyway is wrong.
The only area that a Warrior can claim to be as good if not better in, is enmity generation.
This is not to say Warriors cannot do the same content as Paladins but that they do it with greater difficulty.