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In photography, it's the accepted norm to say that if you know the sensor size of your camera and the focal length of your lens, then you know the field of view of your system.

However, in optics, it's well known that for a fixed sensor size, the distance from the lens to the image plane (which we can equate with the flange distance) also affects your field of view. Everyone who mounted hisher lens on a macro adapter had seen that increasing the flange distance will narrow down your field of view, and they will end up with a macro lens.

So my question is why do we characterize lenses with the focal length and not the effective field of view?

I realize that it could be the case that it was just an arbitrary historical decision, but I'm curious whether there's justification for that which I'm missing.

This question is predicated on a misconception. The flange distance is included in the focal length in lens labels — it is the distance from the optical center of the lens focused at infinity to the imaging medium. This includes the flange distance. (See What is the reference point that the focal length of a lens is calculated from?, and What exactly is focal length when there is also flange focal distance?)

This means that for a given sensor size, lenses made for different mounts are still comparable — a 24mm lens gives (approximately) the same field of view regardless of the mount distance of any given system. So, focal length does correspond to field of view.

You note that using a macro adapter affects field of view. In fact, they also increase the focal length, although since macro extension tubes remove the ability to actually focus at infinity, we leave practical reality and get into the realm of theory.

So my question is why do we characterize lenses with the focal length and not the effective field of view?

The very good reason for cameras is that field of view also strongly depends on the sensor size. A small sensor captures a more narrow view than a larger sensor can.

The lens focal length does provide some field of view, which the sensor size crops to capture possibly a lesser amount of it. Cameras with tiny sensors only capture a small field, so they have to use a much shorter focal length lens to compare to an expected "regular picture" view seen by other cameras with larger sensors. Crop Factor compares that sensor size view to the historical 35 mm film frame size view that so many of us are very familiar with.

Focal length is NOT at all about the mounting flange distance. The internal focus node can be moved by design. A "telephoto" lens means that node is slightly in front of the front lens element (lens is shorter than the focal length). A retro-focus (wide angle) lens places that focus node behind the rear element, to create space behind the lens. But focal length is to that focal node.

The focal length marked on the lens is when focused at infinity. Some imagine that is the definition of focal length, but it is merely one setting for it. Zoom lenses also vary focal length.

When focused closer than infinity, the lens is extended forward (the frontal elements are, or possibly only internal elements) so that the internal focus node in the lens is further from the sensor plane. If we instead assume focal length is the distance from this internal node to the sensor plane, then of course the focal length is a bit longer when focused closer. That longer focal length changes things, like f-number, which can affect exposure, so regular lenses don't allow distances shorter than some nominal close distance, typically at around 0.1x magnification.

Focal length and lens FOV are inherently the same thing. The variable is how much of the lens' FOV is utilized (i.e. extension tubes/TC's/crop sensor/etc). Why would you specify a lens' characteristic by something that may be variable?

The focal length of a single lens always stays the same, the field of view changes as you focus on something closer than infinity, that may be a good reason to specify the focal length, and not the field of view.

I think we use focal length as attribute of lenses fro historical reasons. Time ago glass elements can be measured by distance from the focus (using Sun light) to the "center" of the element. Same is true for the lenses. To get field of view you need to do some mathematics and (maybe) this stop ordinary people (not mathematicians) to use it.

But this question IMHO is too broad and opinion based....