> So what would be the value of having or using indexes other than Integers to index Arrays?

It removes a level of indirection, wasted space, and mental overhead. Suppose you have some table of 'a'..'z' -> whatever. What are your options?

- Switch/case. This may be optimized and fast, but that's not guaranteed across all languages and compilers.

- Hash map. This introduces memory overhead even if it is technically O(1) for access times.

- If in C, you could do:

  T* table = (T*)malloc(sizeof(T) * 26) - 'a'

So that the characters can be used naturally without later modification (not a feature in every language, though).

- Manually calculate each offset every time:

  table[c - 'a'] = ...

With language appropriate type conversions, if needed.

Or you can allow any custom range to work, and do the math in that last option automatically because it's trivial for a compiler to figure it out and it removes unnecessary mental overhead from the program reader and writer.

  table['a']

Just works.

> You can also define integer-valued named constants, and use those if you prefer.

Because everyone wants to see `lower_case_a = 0` and the 25 other cases in their code along with all other possible constants. At least use an enum, sane languages even make them type-safe (or at least safer).