I don't think that is the only backing, it is true that these powers established the backing, but even if the US is entirely a benign empire or just an isolationist republic it would have achieved the same effect given two things;
1. US was very safe and wealthy after the entire planet was wrecked in WWII (which wasn't the US fault)
2. The US is very happy to take debt (provide liquidity, in fact countries were scared once that if the US paid all it's debts the liquidity will disappear) AND be hyper capitalist that will honour its debts and property rights.
Both these aspects basically made the US the biggest most liquid and most reliable market.
Note that London lost its empire but is still a significant market mainly because it insisted on honouring property rights and pay their debts despite the painful price their industries had to pay.
So if the US gave up the empire and only acted as a reliable liquid market, ironically their market hegemony will thrive longer.
The only reason it is not sustainable is because they are using it as a financial weapon and bullying countries with it, so increasingly everyone will try to find an alternative even if not as liquid.
But Bitcoin isn't ready and not big enough to be that thing... Not yet.
