You've argued that the Sun's rate of motion across the sky should have a constant magnitude (under the assumption of an Earth analog with a perfectly circular orbit but still 23.5 degree obliquity). It's not clear to me why this should be the case; on the celestial sphere, I would have an easier time accepting that the Sun should have a constant "horizontal" (i.e., in the sense of right ascension) motion due to the Earth's constant orbital speed, and that the Sun's "vertical" (i.e. declination) motion should be purely sinusoidal: greatest at the equinoxes, zero at the solstices. Have I misunderstood something here?
As an extreme case, imagine a tidally locked planet on a circular orbit of 1 AU with 23.5 degree obliquity. An observer sitting on the equator would see the sun moving on a line overhead, crossing the zenith back and forth, with no figure 8 -- right?