Yea, const provides immutability with respect to assignment, but without immutable objects and collections, it isn't going to get you all the way.

    const a = icepick.freeze({b: "foo"});

Granted, that's not as elegant as built-in support but that is literally what I'm doing at the moment when I want immutability.

So if you go to extraordinary lengths you can use JavaScript functionally but it's not very functional by default aside from the first-class functions. Personally I just embrace it's imperative/functional blended nature and go with it.