Well, actually the Russians ran out of money.
Well, actually the Russians ran out of money.
As a pithy summary of what happened to the USSR, that's not bad. As a summary of nuclear non-proliferation it's ahistorical.
Take a step further back. As Thomas Sowell says, economics is the study of the allocation of scarce goods that have competing uses. In a free economy, money is how we organize that. But even if we had infinite money, that wouldn't give us more of anything else. It would just mean that everything cost infinite dollars to buy.
The problem that the Soviet Union had was that their economy couldn't produce enough to supply their military competition with the US. "Ran out of money" is one way of describing that, but the literal number of rubles in circulation is not at all the issue.