Which ones? Websites that ship no JavaScript? All browsers support this.
> can in some cases completely break sessions
Or you can just remove local storage from window and have it just for yourself, which seems what Discord is doing as well.
Attackers cannot use local storage because there is no local storage on the window object.
> A separate attack vector for the same problem
It's not exactly the same problem. The example you mentioned is a footgun because you don't vendor your dependencies. Deliberately giving someone else access to your website is an issue in itself.