You can’t make that round.

I mean, you could. You'd need three times as many contacts in the receptacle as pins in the plug. Each pin would have to be able to touch exactly 1 or 2 contacts simultaneously. Each receptacle contact would need to programmatically assign itself to perform the role expected for the particular pin it is touching at any given moment.

Pin 1 would start off touching Contact A. As you rotate it, it would connect to A and B. Keep rotating it, it drops A and touches B alone. Then BC. Then C. Then CD. Then D. Then DE, and so on.

Assuming by "jutting pieces" you mean the pins, yeah, I could see that being difficult ultimately to manufacture into the 3.5mm jack configuration.

But translating each pin to a "band" (sorry I'm not very technical myself) on a jack with the form factor of a 3.5mm pin should be doable. You'd probably need 5 or 10 bands since (as I understand it) USBs use a 5 pin connection (again, as I understand it, most devices mirror the 5 pins on each side, but some more advanced/specialized USBs utilized the USB-C connector as 10 pins, hence the possible desire for a 10 band jack).

Again, I could see that being difficult to manufacture, but not impossible, and especially if it became a standard package. Might need a bigger jack than 3.5mm though.