The problem is you're trying to redefine English (and probably most other languages). The first item on a menu is, well the first item, like first place in a marathon, the first day of the month.
Surely a definition of the zeroth item would be something like an item that does not exist, the item that's left when you take away all the other items, etc.
Ordinals are 1-indexed. Language is 1-indexed; The #1 player is the best player, and so on.