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This is not "luckily", it's by design, and there's a couple of other key differences as well.
1.Modern central banking implements an artificial separation between government and CB (an imperfect one), that attempts to make this less recursive...
2. ...but the key difference here is that the value of the dollar ultimately derives from the fact you need to pay US taxes with it. If you want to do business in the US, you need to get some USD to pay taxes in which are then used to keep the US a place to do business in. It is exactly the same model as FTT except that instead of paying "taxes" to trade on one of many market places, the US is a giant nonfungible place, with lots of difficult to move assets and people, serving a fucknormous circular economy with a staggering amount of real world consumption - i.e., a place you want to or have to do business in even if there's shock...
3. ...and has a monopoly on the violence (in the form of laws, courts, police and military) that actually enables the notions private property that enables this all. If the US government collapses your dollars are worthless whether they are backed by a bond or not.
4. Finally, neither the CB nor the government are up for sale or needs to generate profits or shareholder value. All they need to care about is continuing the system in a way that its constituents want (I'm not specifying the aggregation method, oligarchs are still constituents)
So overall, and with the fact that this is a system which has been iterated on for hundreds of years(thousands if you count legal code), yeah, it's a lot more stable