As always, there are both historical reasons mixed with technical issues, notation, and the intelligibility of the score, but in this specific case, also organological ones.
On one hand, the organ, and in particular the pedalboard (its range and its independence), has undergone different evolutions over time; on the other hand, compositions, and consequently notation, have sought over time to better leverage this evolution.
Writing for an organ with an octave of pedals that generally sounds with the manual coupling, this staff is not strictly necessary. There will be few notes, in a single octave, and without difference in color (registrations) compared to the manuals.
In the case, however, where one has at their disposal an organ with an extended pedalboard, many registrations (including 4' stops), apart from the possibility or not of using a wide range, there is the possibility of suggesting the most appropriate registrations within the economy of the piece itself.
This is said succinctly and generally, but in the topic I was referring to the orchestra; however, the same argument can apply to the choir, the band, and some percussion instruments also come to mind. In this regard, the vibraphone is generally written on a single staff, but if the writing is very complex, it is suggested to use two. The same applies to the band; for example, one usually uses a single staff for trumpet 1 and another staff for trumpets 2 and 3. In very contrapuntally dense writing, reading the staff for trumpets 2 and 3 could become difficult, so the composer may consider using 3 separate staves for the 3 trumpets. This can happen with the orchestra, or with the choir (if you have very large divisi, perhaps it is worth adding more staves at certain points to provide clarity).
It just so happens that in this discussion one can also include the issue of soloists: dedicated staff or not? The answer is always 'it depends'.
With these premises, returning to the organ, one could write a piece where the pedal does not have a significant part for organological reasons (absence of a pedalboard, pedalboard with few notes and non-independent) or by choice. Bach himself (but also Mendelssohn and many others) wrote for solo manuals despite having organs at hand that would allow him to do anything. Therefore, a staff might not be necessary; however, understand that if the piece were serial, the only 5 notes played by the pedals are structural, and every time you want a different color from the parts given to the manuals, that is when the staff might still become necessary—even though at a note-reading level it wouldn't be needed, it would precisely be the organistic orchestration that dictates it.
In short, no real rule exists; there is, on one hand, the creative work of the composer and, on the other, the need to put the performer in the best possible conditions. A complex work must nonetheless result in being intelligible.
I often read: 'I wrote it this way because it's convenient for me.'
No, No.
Writing a score serves to communicate one's thoughts to the performers who must realize it; therefore, those who must be 'convenient' or rather, put in a position to fully understand your thought, are them. Thus, there is no question of one's own convenience. Unless the score is a sketch, intended for oneself or destined to stay in a drawer forever, the argument does not hold.
And just to return to the LAB, posting the score in a forum already means, for me, being 'out of the drawer'.
This is what came to mind, and I have tried to write it in a haphazard way; what do you think about this issue?