Petrodollars don't underwrite demand for American dollars. American consumption does. People have dollars because Americans buy with them. This wide base of dollar holders produces a deep and liquid international market.
Compare that with the Euro, which has France threatening to withdraw, and the Renmimbi, which Chinese will sell at fire sale prices for access to international markets their government prohibits them from accessing.
Petrodollars once played a role, but no more. Frankly, it seems like an unnecessary liability held over from when the American economy was dependent on foreign oil.
Good question, and it's one I'm interested in as well.
I've uncovered some interesting references on the UK monetary crisis of the 1970s -- the UK required an IMF bailout, though revenues from North Sea oil sales helped considerably as well.
There is a bit of similar discussion about US monetary policy from the early 1970s, and I've a stash of J. Econ Rev. or similar articles from economics conferences of about that time which touch on the question, though I'm not sure the information's good.
Steve Keen has good insights in a few areas, as does David Graeber. I've got Keen's book handy, and will take a look through it.
Otherwise, there's the story of devaluations of other currencies throughout history. Joseph Tainter, whom I've mentioned elsewhere in this thread, has a long bit online (YouTube) on the devaluation of the Roman denarius -- specie coin which fell from 99.9% purity to less than 4%. Adam Smith talks of the inevitable debasement of coin in Wealth of Nations. And Robert Newman (a comedian, not an economist, though his work here is excellent) touches on petrodollars and sensitivity regarding them in his History of Oil: https://m.youtube.com/watch?v=GIpm_8v80hw At 21m30s.
Hrm. Nothing in Keen on "petrodollar" or "Bretton Woods", and only a brief, 1929 reference, to the gold standard.
I'd suggest looking up J.K. Galbraith or Philip Mirowski as possible sources, though I'm not aware of anything specific to either of them. Highly-regarded and unorthodox economists.
Compare that with the Euro, which has France threatening to withdraw, and the Renmimbi, which Chinese will sell at fire sale prices for access to international markets their government prohibits them from accessing.
Petrodollars once played a role, but no more. Frankly, it seems like an unnecessary liability held over from when the American economy was dependent on foreign oil.