The distinction, and this is an important one, is that cookies have a hard cap of 4Kb of data per domain, making them nigh-useless for that purpose. All they are good for is recognizing a given user server-side across multiple page loads and storage of a few handful of user preferences. Cookies also get sent with every request, so using them as storage is just asking to balloon your bandwidth costs.

On top of that, using localStorage for storing large amounts of data rarely involves anything like a cookie warning because it's 100% client side unless manually sent back to the server. And even then, if you anonymize the data (i.e. you don't care who's storage you are using), you still don't technically need any warning.

All this to say: There is basically no relationship whatsoever between pervasive cookie warnings and the usage concerns you are voicing. Both are valid concerns, both are important stakes, but they have nothing to do with one-another.

You do say hard drive but you also imply that permission to store cookies is as good as permission to mine cryptocurrency simply because the user allowed access to storage.

The argument these other commenters are trying to make hinges on the idea that the type of storage for cookies wouldn't work that well for crypto mining.

You're calling that argument nonsequitor and I don't think it is. It's immediately applicable to explaining the gap in your reasoning. That gap, for the record, being Cookies Storage == Crypto Mining.

Finally, let me give an example. "I own my house and my land so therefore I'm a sovereign citizen." That's a bad argument for largely the same reasons.