Range anxiety is solved by building out charging infrastructure. There's no range anxiety once you can rely on there being fast, convenient, reliable charging stations along all the routes that you will conceivably travel on. If you're running low then you just stop and charge wherever, and whenever, it's convenient.
You'd have range anxiety about gas cars, too, if there wasn't a reliable network of filling stations on the routes that you are travelling!
You'd have range anxiety about gas cars, too, if there wasn't a reliable network of filling stations on the routes that you are travelling!