Because otherwise you would be wasting a perfectly good number for no reason, which means you need to use more bits to do the same thing.

To write 4 numbers (including zero) you only need two bits

    0: 00
    1: 01
    2: 10
    3: 11

To write 4 numbers if you avoid using the number zero, you need three bits

    1: 001
    2: 010
    3: 011
    4: 100

If you extrapolate that a little bit, you'll realize that you'll need two bytes (1 Byte + 1 bit from another byte) to store the indices of an array with 2^8 elements, which is just dumb.

Some of you might be thinking: you don't need to store it the same way it's written, you can just substract 1 from whatever the user typed and convert it behind the scenes.

Yes, you could subtract 1, but then you would be making the whole system more complex, opaque, and unelegant, while hiding information from the programmer for no good reason.