Yes you are right.
It is enough to leave only two shafts.
I have a paradox. When I set the rotation to 360 degrees, the two shafts only rotate 180 degrees. All body rigid:
If I set 720 degrees they make one revolution.
But if I add a shaft to the wheel, then the shaft slows down and the wheels spin in place:
I made animations (see above) but they don't work on the site
attached them as files: