So to clarify for people unfamiliar with NA12878, that's the sample identification for a particular Utah woman. Her parents are NA12891 and NA12892. In human variation data-sets that's what we are given to identify individuals, an ID, sex and population. All the other data is removed to protect patient privacy. So the question is why was NA12878 (this Utah woman) chosen as the reference patient in genomic analysis...
I don't know the real practical answer but from what I gather it's inertia.
I don't have a full history for her but I do know somethings which make her genome a good choice for a benchmark. NA12878 is a fairly old to geneticists and her DNA is included in multiple legacy projects, specifically HapMap.
She has a genetic disease (CYP2D6 mutation) which is probably what initially included her and her family genetic analysis. This is a better reason to study this genome in detail instead of it simply being someone famous (i.e. Venter).
She's Utah mormon (small founder population with extensive pedigree information), has 11 children (can do recombination/inheritance analysis). What this means is that a deep understanding of her genome will have applications to this population.
Her lymphoblastoid cell line GM12878 was included as tier-1 ENCODE cell of study. This means there's terabytes of epignomic data for her as well.
When I choose to do human genome analysis, NA12878 is the obvious choice because of how much data is already available, which also means more data is going to be available. Thus I think the answer is largely inertia.
Also consider it this way, if you're trying to say your pipeline or sequencing technology is better then other ones, and everyone uses NA12878 to benchmark their technology, then it's wise to also use NA12878 so the results can be comparable.