The dollar is backed by the petro-dollar, the fact that Saudi Arabia and friends only accept dollars when selling oil is one of the reason the dollar is strong. When you factor in that the US military protects the petro-dollar while at the same time being the biggest consumer on earth of oil, it starts adding up. Europe and therefore the Euro is also protected by the US army. All of a sudden, your fiat's energy consumption is probably much bigger than bitcoin ever will be.
It's not like we'd stop protecting our oil supply if we converted to Bitcoin. We'd still need oil for cars and planes and so on. If we manage to stop using oil, we won't need the military to protect it anymore, even if we haven't converted to Bitcoin.
So I don't think we can lay the military's oil consumption at fiat's feet.
It has nothing to do with protecting the oil supply. The U.S. military is deployed to ensure that oil producing countries don't go and sell their oil for anything other than dollars. Protecting the oil is completely orthogonal.
The dollar being strong or not doesn't change the fact that a transaction in any currency is several orders of magnitude more energy-efficient than with bitcoin.
About 40000 times less I think? That's the figure I saw for a SEPA transfer or Mastercard transaction vs the bitcoin equivalent