The rules allow it, but the rules allow it because no one ever thought they needed to disallow it. Not because the designers found some value in allowing it.
Hmm, well as to speculation about designer motives, I take the "value" in this case to be found in the properties of the whole system. As a designer, given
A. I want to allow characters to multiclass including choosing multiple spellcasting classes
B. I want spellcasting characters to have preferred access to subsets of all spells (e.g. a class spell list)
C. I want to offer feats to characters that give limited access to subsets of spells
D. I want to offer class and sub-class features that modify or act upon subsets of spells
Contemplating design goals like that, it seems obvious that a clean approach would be to separate spell lists out from classes and simply state what list a class or feat was to draw from. Unfortunately that provoked backlash, so they reverted to the more traditional approach.
Either way, unless one engineered in a clunky extra rule to forbid it (limiting without removing multiclassing) or did something even clunkier like counting spells as appearing on different lists for specific purposes (like multiclassing) duplicated-spells are just an emergent feature of the whole system. An elegant approach would be simply
don't support anything like A. and C.
The value (of allowing that emergence) is found in what the whole system affords, such as if I multiclass spellcasters I can cast spells from each of my lists up to the appropriate level for that list, applying whatever features I have that modify spells to that list. Were it not for duplicated-spells, multiclassing would allow for even stronger, less-balanced, characters than it currently does. Another aspect of "value" is the "designability" of the system: I can avoid increasing the playtest burden because I don't have to consider every possible spell when I design a feature that does-something-with-spells. I can constrain it to one list.
The value is in the overall design space afforded, not specifically (and really, as you point out) that players ought to be able to make what would amount to trap picks. While I see (and have played) a few cases where duplicated-spells turned out to be worthwhile (or at least, seemed so to me) that's not really what I wanted to argue. My analysis was more about seeing what the game system unavoidably contained (duplicated-spells) and what else that implied.