Yup, you're on the money here. In fact browsers should make accessing the data stored by sites and modifying their permissions drop-dead intuitive, even for non-tech users and those with more knowledge should be afforded further knobs to tweak. This kind of UI might be a bit hard to design and require some thought, but I think it is quite possible, and I find it surprising that even after all these years, the dialogues and preferences dealing with examining and controlling the storage and execution of websites and apps to be poorly thought out, obscure and very clunky.

I can understand why Chrome might not want to improve in this regard as its parent company's interests directly conflict with more user control of web data, but amazingly, if anything, Firefox's settings for auditing and restricting websites is even worse. And none of the browsers, AFAIK, have taken the initiative in this area and tried to really differentiate themselves.

I suspect they think no one except a few tech users will be interested in these knobs, but the thing is, if you make them prominent, easy to use, understand and intuitive, I bet a lot more people will start using them.