Equivalent FL is not a measure of an angle of view. It is a measure of what FL on the reference FF format would give the same AOV. FL or equivalent FL translates easy to magnification (similar triangles); there is also the tradition as a factor.
In other words, you are saying:
Equivalent FL is not a way of measuring AoV, it's a way of measuring AoV. This statement seems to have a logic problem.
No, I am not saying that. My logic is fine.
Well now we are into the weeds of discussing semantics. We agree that Equivalent FL is a "measure". Where we disagree is what it is a measure of.
Getting back to the driveway analogy, I think that if we describe the length of the driveway in terms of Chrysler Minivans, then that is a "measure" of the length of the driveway, and the units we are using are "Chrysler Minivans".
In photography we talk about "wide angle", "normal", and "Telephoto", lenses. These are descriptions of their angle of view. The general rule is that a "Normal" lens is one where the focal length is about the same as the diagonal measurement of the film/sensor size. Shorter focal length are classified as "wide", longer are "telephoto". A 50mm lens can be wide, normal, or telephoto, depending on the film format (sensor size) it is being used with.
When we say that a lens has a "50mm Equivalent FL", we are saying that the combination of that lens on that format has the same Angle of View as a 50mm lens on a 35mm film SLR. "50mm Equivalent FL" is a measure of Angle of View, in the same way "4 Chrysler Minivans" is a measure of driveway length.
You seem to be making a distinction based on the fact that the measure is based on a standard reference model.
I can measure how long my driveway is in either feet, or Chrysler Minivans. Both are a valid measurement, even though the later is based on an arbitrary standard.
Actually, the latter could be more useful.
Only if you are very familiar with Chrysler Minivans. If you drive a Miata, a length in feet might be more useful.
But if your parents drove Chrysler Minivans, you might be in the habit of measuring driveway lengths in units of Chrysler Minivans, even if you and your friends are all driving smaller cars.
Equivalent FL really is a way of measuring AoV.
No, it is not. If you want to relate it to the AOV, you get a nonlinear relation. If you are shooting with FF, you skip “equivalent”. When you say 24-105, you mean exactly that, focal lengths.
There are lots of measurements that are non-linear. For example f/stops. Double the f/stop and you quadruple the area of the aperture.
Sound volume is typically measured on a log scale. Increase the sound by 3db and you have doubled the volume.