Adding a warning upon localStorage would be like adding a warning upon setting cookies. The banners that websites add for setting non-essential cookies are annoying enough already without having to click past browser permission screens for essential cookies as well.
Also note that privacy laws or "cookie laws" don't ever mention the word cookie. If you are being tracked using localStorage, canvas fingerprinting, ETags, etc., they have to disclose the tracking. Not the method, I think, but what data they are collecting, for what purpose, with which retention period, and what their legal basis is (e.g. "we collect your address on the basis of fulfilling the contract to ship your package" or "we track you on the basis of consent"). LocalStorage is not something to be more or less afraid of than cookies, etags, etc.; the browser doesn't ask for those either, and I personally think that's better.