Earlier quoted context omitted.
Starting with 0 is quite common in series, e.g. Taylor, Fourier, Chebyshev expansions, etc.
No... in those cases you're starting with 0 because that's the lowest exponent of a polynomial.
What index to start with only strongly matters when the indexes have semantics. Otherwise you should just treat it as an opaque index, i.e. eachindex(), keys(), etc. In math when there are semantics, the indices usually include 0. When not (vector components, matrix indices, etc), they usually (but not uniformly) don't.
The one nice side-benefit of Julia's mistake in adopting 1-based indexing is that it provided an extra impetus to build machinery to handle arbitrary indexing, though too much code still doesn't work correctly, and code still gets written to only handle 1-based arrays.