That is correct that Drk Aoe uses mana. I deliberately pointed out that a War will run out of mana if they're pushing for their tp inefficient skills.
In the case of simplying using your Sword combos, Drk would have to use a mana GcD skill to replicate what is a natural effect for warrior, using a tp less gcd spell.

Another way to look at it would be that Drk has less initial tp cost due to building aggro via mana, but more sustained tp useage otherwise.

Could be a wash either way, but War regardless regain TP on every IB.