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I never understood this until now. Thank you.

... what makes stellar day real, ... ?

It's not really real, just side-real.

Oh man this was the pun of the week. Well done.

You won the internet today, sir.

"Real" is not real.

A solar day is still not exactly 86,400 seconds long.

I think there is a misunderstanding somewhere in here. m0skit0's comment was contrasting sidereal day (23h 56m 4.100s) to the original post concerning a mean solar day (24 hr 0m 0s). rimliu's comment seems to be saying that mean solar day has advantages over apparent solar day (each day has a different number of seconds that average to 24h 0m 0s over a year). I love the equation of time, but it is not related to sidereal time as discussed.

Small correction to m0skit0: wikipedia says the sidereal day is 23h, 56m, 4.0905s to account for the 26,000 year procession of the March equinox.

I also mention measuring days with regard to the start we are orbiting (Sun and solar days) compared to the distant stars (sidereal days), so no misunderstanding here. Once again it is about having Sun at more or less its highest point in the sky at noon. With sidereal time it would constantly shift and if you had sun highest at noon today, if would be highest at midnight half year from now.