It has as much need for it as the dollar, which is either "both need it" if you're focusing on the warfare part and using "petrodollar" as rhetorical emphasis, or "neither needs it" if you're focusing on literally the support of petroleum and using "warfare" as rhetorical emphasis.
"Both" is because guns beat bits. Or, to put it another way, if the USA had used Bitcoin instead of dollars in 1960, the Soviet Union would've been just as much a threat, and similarly the forced nationalisation in Cuba after the revolution would've happened no matter who recorded what on any blockchain.
"Neither" is because petroleum is just one of the major energy sources of the last century, vital for the industrial strength of the US economy and its capacity to actually make things worth buying (in addition to uselessly trinkets), but not the power source of the next century.
No, there is an asymmetry you are missing. The "well the dollar has an army behind it" is only extremely narrowly relevant to anything, in that the US can force dollar settlement with the military. This is only necessary because people either don't trust the issuer or don't want to pay seigniorage fees to the US. Neither of these is relevant for btc.
"Both" is because guns beat bits. Or, to put it another way, if the USA had used Bitcoin instead of dollars in 1960, the Soviet Union would've been just as much a threat, and similarly the forced nationalisation in Cuba after the revolution would've happened no matter who recorded what on any blockchain.
"Neither" is because petroleum is just one of the major energy sources of the last century, vital for the industrial strength of the US economy and its capacity to actually make things worth buying (in addition to uselessly trinkets), but not the power source of the next century.