SWIFT is a communication network, it replaces the letters and couriers ancient banks would have used to agree that payments have been ordered and funds have been moved. Payment don't "go through" any bank that hasn't been explicitly requested. The whole point of the SWIFT network is that it is global and it allows you to reach every branch of every bank.

There are of course banks whose SWIFT processing is handled by someone else, but they are usually service bureaus or central offices within a conglomerate, not partners in a specific country.

I'm not sure about this. I think you're conflating SWIFT transfers with USD transfers

USD is fully convertible https://www.kantox.com/en/glossary/fully-convertible-currenc...

I can "take dollars out of my pocket" and pay you without going through the US no problem

USD transfers even within same non-US based bank let's say same example in Poland is done with SWIFT, but unlikely it goes thru NYC bank as the cost is none and the transfer is instant. SWIFT is used only for addressing and accounting in such case.

Within the same bank it's just internal accounting. But when two different banks are involved, an USD transfer generally goes through USA.

No it doesn’t, https://en.m.wikipedia.org/wiki/Eurodollar.

Not to mention that since the USD is a CLS/FCC currency you can perform correspondent banking transactions with it without having any government involved in the process.