It does make sense from that perspective, even if the writers weren't intending to make a critique of capitalism. Maybe more so.
To give an overview, capitalism's most important contradiction according to the LTOV is probably the tendency of the rate of profit to fall, which takes the form of recurring accumulation cycles, ending in crisis, and recovery to start the next cycle. Initially accumulation crises were resolved by mass bankruptcies, the "business cycle", which grew larger and more spaced out as the mass of capital accumulated. In the imperialist epoch (which started at some point around 1900) the mass of capital is so large its crises can only be resolved by generalised war, which increases the rate of exploitation, suspends competition, and reduces the organic composition of capital (you can read more about all that
here if you're interested). The most recent accumulation cycle ended in 1971, and the crisis has been building up (with countless moves to delay the inevitable, intentional and accidental) for 50 years now. Note - this doesn't mean wars are an insidious bourgeois plot to restore the rate of profit or something. The wars happen for a reason that goes hand in hand with crisis - imperialism.
Capitalism in the crisis definitely rubbed off on Fallout. Automation and capitalist offences - both attempts to reduce variable capital (wages etc) - are prominent features of our world and FO's. So is the lack of a working class response (76 actually has some evidence of action and resistance, which is a nice touch). The Resource Wars resemble the imperialist regional wars of our time blown up to nuclear proportions. The conflict in the European Commonwealth and the Sino-American War only highlight the scale of the hypothetical crisis, which by 2052 (dissolution of the UN) is so immense the delusion of Western and Chinese exceptionalism and the desperate attempt to keep the inevitable war from happening collapses. In the absence of revolutionary consciousness, global destruction in a generalised war, the Great War, seems inevitable - which, to be fair, isn't that far off. You could interpret Fallout as a warning, or a cry of despair.
The moral definitely wasn't "if you replace the shit you're running out of with different shit it'll all be okay, otherwise the world will end". Oil was only a catalyst.