Natural language isn’t precise and a lot is inferred from context. Exact order does often not really matter. In formal languages, however, you want to be as unambiguous and exact as possible, so it makes sense to use syntax and symbols to emphasize when elements differ in kind.

Incidentally, that’s also why we use syntax highlighting. One could, of course, use syntax highlighting instead of symbols to indicate the difference between function and arguments (between operation and operands), but that would interfere with the use of syntax highlighting for token categories (e.g. for literals of different types).

We also alternate between various positions in programming languages, so it's not a matter of formal precision.

Not sure what you mean by “alternate between various positions”.

Prefix for function, infix in expressions, and postfix if you use forth