The old 5 saves were confusing when you needed a save for something that isn't explicitly covered in the categories. Yes, if it's a listed effect it's quite clear what you use, and certain saves take priority when there is overlap, but it's not always the case. I had that problem all the time when I set up traps; if it's not one of the listed effects, what save do I use? I got this pit trap here (and this came up often because I like pits a lot), what save is appropriate? It's not poison, it's not being shot out of a wand or breathed at the PC, it's not a spell, and it's not transforming them. I'd end up picking whatever I thought the PCs were more likely to fail TBH. With F/R/W it's a lot easier for the DM, saving against a pit is really a matter of dodging or avoiding something, so it's obviously Reflex.
Well, by the O(A)D&D rules, there isn't a save for traps, unless that trap involved one of the list of saves. (A poisoned needle, for example.) Now, depending on what version of the O(A)D&D rules you were playing, there may or may not have been a baseline rule for determining whether a trap takes effect. For example, in the 1981 B/X rules, traps were triggered on a roll of 1 or 2 in 6 anytime someone does something that could trigger the trap. (Walk on the pressure plate, stick a key in the hole, whatever.) In other versions, it was at the DM's discretion to determine whether the trap took effect, and various DMs and module writers used various means; to hit rolls (the trap struck like a x level fighter against AC whatever), rolls against attributes, and, yes, the saving throw chart, among others. But those were not "real" saving throws used for the same purpose as other saves, but rather a cobbled-on mechanic to determine whether the character was effected by the trap.
I think the ad hoc use of the saving throw chart in this manner obscured what saving throws are supposed to be in O(A)D&D. Saving throws come after it's already been determined that the character has been effected by the threat. The dragon breathed, the spell went off, the character met the medusa's gaze, he got bit by the poisonous snake, whatever. The roll is to determine whether the character survived. Thus "saving" throw. The character is already "dead." Can he now be saved? Gygax spends about half a page on this in the 1e DMG, starting on the second column of page 80.
So should there have been a saving throw against falling damage? Probably not, because it was rarely the type of threat that would result in automatically taking the character out of the game. You rolled damage instead, just like if the character was hit with an axe or sword. (I'm not sure the mechanic in post-2e D&D, but it was notoriously difficult to kill pcs with falling damage in O(A)D&D, unrealistically so.)
So, to put it another way, the saving throw in O(A)D&D was supposed to be more akin to rolling the damage dice than to rolling the "to hit" dice. When you were rolling for a save, you knew that your character had already been "hit." You were determining the effect of that hit with the saving throw.
