The natural numbers are generally considered to start at 1. Therefore, to people in general, such a system makes more sense.
Zero is not a "natural" number, in fact many societies / civilizations never even understood or used zero in arithmetic [1].
Yeah, but those societies were uniformly terrible at math.
If I hold up my fingers to indicate elements in an array, zero fingers means the array is empty. One finger is then, naturally, the first item: of index 1.
Counting elements starting at zero (for the first element) is still unnatural...
And you only need 1...N to order N bins and their contents.
Of course, most programmers don't have math degrees and I'd suspect that most people indeed think 1st element of an array starts at 1.