I regularly transfer money from AUD to IDR or EUR, and from Australian bank accounts to Indonesian or Euro, without any apparent transition with US intermediary banks and USD conversions. I did surprise someone from Eastern Europe when I was in Indonesia that I had never touched USD, so I guess in some parts of the world USD is important.

Many of my non-mediated transactions go through American institutions (e.g. Mastercard, Visa) but not all.

And if anything does go via USD I don't notice it, even in price; it's clearly cheaper to go AUD->IDR than to go AUD->USD->IDR.