^
Not really.
Pretty much it boils down to Blood Price is your MT in Grit MP regen, Blood Sword is your OT out of Grit MP regen. There is of course some level of flexibility but it is pretty obvious that is their design. Blood Price is just one of the base ways to regain MP, not something extra like Infuriate is, it just happens to shine in such a situation.

Yes, you gain lots of MP back from Blood Price while getting hit by lots of mobs in trash pulls but that does not help with boss fights and does not function like Infuriate which essentially is a one button "I get to do a special move now" ability on a mediumish length cooldown timer. That is what I was saying would be nice to have because it provides a more similar, yet still different, equivalency between WAR and DRK when it comes to mechanics since those function the most similar of the tanks. WAR being a build up resource (stacks) tank and DRK being a burn through resource (MP) tank.