I don't know of any paper trying to explain why click consonants might have developed in languages in the first place. But something to keep in mind is that most languages I know use clicks as non-segmental signs, for instance the English interjection tsktsk, or the way you call a horse. Germans have a bilabial click that indicates something like "tough question/don't know". Intuitively I have a feeling that clicks are very iconic (for instance the click we use with horses somewhat resembles the sound of a gallop, the disapproving tsktsk that of a slap), but my intuition might be wrong and I don't know of any studies on this. Acoustically clicks are quite distinct in the signal, meaning even in difficult conditions they should offer high recoverability compared to say a fricative. On the other hand, complexity comes with a phonological price tag, so such an argument in phonetics has a counter argument in phonology. I could imagine that acoustic distinctness/recoverability is a good thing under difficult conditions (e.g. noisy environment, dense forestation) or communication over a long distance, but whistled language is generally a lot better for this and the environmental conditions around click-rich languages do not really speak for this being a factor.
There is a paper here which suggests that clicks don't offer any acoustic processing advantage per se in languages where they are not used as regular segments. And this paper has a nice overview of literature on linguistic change involving clicks, which might be of interest, but doesn't offer an answer to "why"--in fact one may see this as partial evidence that because clicks are segmentally complex they might be difficult phonologically.
Regarding the question of whether clicks were part of a hypothetical proto-human language and then lost elsewhere to be only retained as non-segmental signs, see Knight et. al.'s (2003) paper arguing that this is the case, from a genetic perspective authored by geneticists and anthropologists. And then compare this with Tom Güldemann's (2007) paper in ULPA responding to that very paper, from a linguistic perspective, arguing that there isn't really that much support for that hypothesis.