I'm having a difficult time understanding this. I trust that you're knowledgeable about the topic given your comment history, but --
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?
It is quite difficult to visualize and it took me a long time to "get it".
The path of the sun's annual motion relative to the stars is determined solely by my physical progress in orbit around the sun. A planet's axial tilt only changes the 'direction' I'm looking in and thus the reference point of my celestial coordinate system. The sun's path will always be a great circle on that celestial sphere (and always the same relative to the fixed background stars) regardless of which reference frame I choose. I think this is enough to surmise that the sun's angular speed on the celestial sphere is constant regardless of axial tilt (assuming a perfectly circular orbit).
Taken to an extreme, imagine a planet with 90° tilt -- the sun would move vertically and pass directly over the pole, making a constant 'horizontal' motion literally impossible.
I'm not sure what your tidally locked example is meant to demonstrate, since that's literally what the analemma is -- the path the sun would make in the sky once you subtract a planet's local axial rotation, i.e., tidally locking it to the orbital parent.
Thank you for the further explanation - this has convinced me that it's plausible, though my mind is slow and I still need to think about it to be fully convinced.
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?