That TLAR doesn't look right

Part of why 45* is discussed is that it is easy to reference within an aircraft.
Look at most of the round gauges with 4 screws "at the corners", a line drawn through the diagonal screws is 45*, thus easy to see.

Pattern should be taught, "Downwind track (meaning path over the ground, not fuselage alignment) parallel to the runway looking down at the runway ~45* angle.
Turn base when the touchdown point is ~45* behind you.
Turn final when you think it's time, allowing for wind drift.
Reference an aiming point (that is ~200' short of where you want to touchdown) on the canopy, adjust glide so the reference is stationary on the canopy using divebrakes and/or slips.

There will be adjustments in the pattern due to wind, lift & sink.

Why is this taught (assuming the instructor does any sort of cross country)? Because you have no real clue what the "off field elevation" is, so the altimeter is sorta dead weight.
Angles always work.
They work for a 2-33 (steep is fine) and 50:1 glass (a bit shallower is also fine).
But the angles work pretty much regardless PROVIDED your speed is reasonably close, you watch the angles (is it trending steady, getting steeper, getting shallower, etc.) and adjust as required.

I've been using the angles for decades.
I taught the angles (as a CFIG) for about a decade.
I've landed off airport more times than I want to admit. I have to yet overshoot or undershoot my predetermined landing spot by more than maybe 50'.

PS, "aiming spot" gives you a reference so you have a bit more time/distance to "flair to land".

I will have to reread the referenced article to see if I really see an error. I have seen a "power plane" diagram that basically showed that the "aiming spot" was where you were to land. Land hard maybe, but not at a minimum speed.