Since this doesn’t address most of my points, but bring up separate ones, I’m wondering about a few things. What syntax do you think should be used to “index” a Map? Scala supports and encourages functional programming, but it doesn't see it as a silver bullet, hence it allows mutation and side-effects. Most of your complaints here would go away if it weren’t for the mutation. Do you consider the inclusion of mutation to be a design flaw?
Also, on the bounds, arrays in most languages have bounds of [0, length). I’m going to assume that you don’t think indexing with [) would be ideal to match the mathematical notation.