Already exists in some countries (for example in Poland). Each company that wants to keep your data here has to get your permission (either by off-by-default checkbox on a website form, or on paper), and to allow you to delete or change your data in their database on your request.
There is inspector that is responsible for receiving complaints about companies that don't comply with this law, and he can issue warnings and fines to companies. It's working OK, I don't understand why USA would start trade war over sth like this.
As a web developer for a smallish company with detailed customer records I'm happy to add this as a feature.
I'm not sure what to do about my backups but hopefully common sense will prevail on that front.
I'm also curious about industries that need to retain all financial transaction records for a certain amount of time. They are going to have to be exempt from this as well.