It may not be an arbitrary number in the context of the whole instrument layout, but I call it that because I believe the term "scale length" should
directly and accurately describe the fretboard without inclusion of elements which may vary from instrument to instrument. Varying amounts of compensation between different instrument styles (electric, acoustic, classical guitars, banjos, etc), as well as which point in the compensation range (treble string, center average, bass string) is chosen to include could result in the same fretboard being described as different (and often rounded/imprecise) scale lengths. My feeling is that this only makes the term somewhat vague, less precise, and occasionally confusing.
I've posted this excerpt from a paper of mine on other forums, but I think it best describes the dilemmas I see in terminology here.
Quote:
Though it may seem a basic and fundamental point of fretted instrument design, “scale length” has become (or perhaps always been) a rather ambiguous term in the field of fretted instruments. There are in fact several distinct definitions applied to the term by different companies and technicians, as well as some common usages which I hesitate to qualify as proper definitions. The Martin Guitar Company’s use of the term is a prime example of this*.
At least for the purpose of this writing, I will clarify my own definitions of two distinct descriptions of scale length that are most commonly used.
Base Scale Length: The base number from which the fret spacing is calculated. In other words, it is the original length from which the fret scale (i.e., rule, template) is laid out.
Relative Scale Length: 2x the distance from the nut to the center of the 12th fret. This definition does not always directly determine or reflect the spacing of the frets relative to each other. Though this is probably less pure a definition of scale length than the former, it is generally considered the more useful of the two, and certainly more widely used. It's value lies both in it's ease of calculation, as well as it's ability to provide consistent comparisons between boards of different fret placement systems. Assuming all setup criteria remain constant between them, and intonation is conventionally adjusted to 0¢ offset at the 12th fret, the same relative scale length will result in the same end string length, even between boards of different fret spacing systems or nut compensation.
*In efforts of disambiguation, at least one other common use of the term deserves to be mentioned. The Martin Guitar Company defines their “scale length” according to the open length of the high E string, including average compensation (of approximately .060”). This method of defining scale length as the total length of a string is likely carried over from non-fretted relatives such as the violin. On fretless instruments where there are no frets to govern the total string length, the string length of course will instead dictate the fingering positions. This makes defining scale length as the total string length both appropriate and necessary as a relative term for comparing these instruments.
On fretted instruments however, I feel this usage suffers great inadequacies. Foremost is the fact that with a system of straight frets, each string will require a different amount of compensation, and end at a total open length different from others. This leaves the rather arbitrary choice of which string or point along the saddle one chooses to refer to. Martin uses the total high E string length today, but you will hear of others using the average among all strings, and still others choosing the low E. Furthermore, the end length with compensation will change relative to details such as setup or string choice, presenting us with the possibility of the same instrument being describable as several different scale lengths dependant on changes in these details.
While it is unlikely we will see this usage of the term disappear, I feel it best reserved for use as a layman’s approximation. It carries little to no benefit in any technical discussion, and can serve simply to confuse when any need for accuracy is involved. I have personally encountered cases in which small builders have misplaced their bridge, where the fingerboard was sold as a “25.4” scale, and the saddle template labeled the same, but the two used incompatible definitions. For purpose of technical discussions therefore, I prefer to omit this usage entirely, and reserve the term “scale length” to either the “relative” or “base” definitions listed above.
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If a board were slotted to the modern standard of 2^(1/12) spacing and the nut located accordingly with no compensation, the Base and Relative scale lengths would be identical. When a board is spaced to an alternate system such as the true rule of 18 however, the relative scale lengths would indeed be quite different, even though they began with the same base scale length.
For example, if a spacing were to start from a 24.75” Base Scale Length, and use the true rule of 18, the 12th fret would not fall at the halfway point of 12.375” as it would using the 2^(1/12) rule. Rather, it would fall notably short at 12.285”, and in order to intonate properly at the 12th fret, the bridge position would need to be adjusted accordingly. The same 24.75” Base Scale Length is used in each scenario, yet the Relative Scale Length of the “rule of 18” board would end up at 24.57”, while a 2^(1/12) spaced board's relative scale would remain at 24.75”. This is in fact where much confusion occurs in the labeling of scale lengths on Gibson guitars, and demonstrates the need to distinguish the two definitions as independent.
I realize I do not have authority to unilaterally impose my preferred definitions on the whole trade, but that won't stop me from trying.

General use of the term "scale length" has always been rather vague and arbitrary, which is fine for sales literature and layman discussions. For technical discussion within the trade however, I do feel there is a good argument for more precise definitions as those I've proposed above.
If one decides to order a Fender style board cut to 25.5" scale length, or cut one themselves, it would be highly unlikely (and entirely incorrect) that they would calculate the fret spacing based on 25.44". Is it reasonable or intuitive then to expect one to use 25.34" for the base number when using a Martin style 25.4" scale? You can see how this could (and has) easily lead to confusion due to inconsistent use of terminology within the trade.
As to usage of the rule of 18 that late, believe it or not, Gibson still uses it on their electric guitars to this very day. When I first discovered this I couldn't believe it either, but they are still cutting boards to a very precise 24_3/4" base scale spaced to the rule of 18, which results in a relative scale of 24.57" (their Montana acoustics are 24_5/8" with modern 17.817 spacing). As to Martin, their boards measure consistently to rule of 18 spacing up through some time around mid to late 1977. Seems strange, but it's true.