IMO, the typeof operator is just broken. It treats "null" as type object, and it treats functions as a different type from objects (a function is an object, so it really doesn't make sense to have typeof myFn === 'object' not be true). Adding more features around this operator would just further establish its broken type-categorization system.
What I would really like to see, and something that's been discussed a bit elsewhere, is for the language to add a replacement to the typeof operator. Perhaps, as part of that discussion, needs involving the ability to programmatically access the different available types without hard-coding a list of types can be addressed
Though... to be honest, I've never actually ran into a concrete use-case where having a way to programmatically get my hands on all of the possible outputs of typeof would be handy, so it's hard to picture the utility of that.