It's always the second flip

The first flip collapses the wave function so that it has a definite orientation at all. The second flip then achieves the correct orientation.

The wavefunction collapses on the first attempt to plug in: it's always the wrong way.

If that were true then it would work on the second try. In reality it's always the wrong way on the second try.

The second flip is to rotate it around the 4th axis.

nope.. its symmetrical about a bunch of axes. at most they'd need a 60 degree rotation, not 180 like USB-A. So this standard is precisely 3x better than USB-A

How many times better is a barrel jack?

infinity times better, obviously.