Array indexing is a function call, because an array is a function from its index set to the set of the values the array stores, or -- equivalent -- a partial function from integers to the value set.
Scala gets this right.
I don't know, I never liked how all FunctionNs are sort of "unofficial" partial functions (because they may throw), and PartialFunctions are then made a subtype of FunctionN, because they have an extra method where you can ask whether they are defined at given points. Especially since throwing seems to be falling out of favor in Scala, being replaced by Try[] return types.
You wrote that array indexing is "a partial function from integers to the value set". If we're to take the suggestion seriously, then the practicality of it depends on how partial functions are represented in the language. Which itself is certainly not orthogonal to the Try-vs-exceptions issue.
I was talking about the mechanism for array indexing. In both cases, indexing is function application. So the choice of error representation is orthogonal. This is even more evidence that we should not use a different operator for array indexing as Rust does alas.