This is an absolutely stupid notion IMHO because if somebody has the data there’s NOTHING you can do to stop profiling. The right to the deletion and security of your own personal data is what needs to be protected. This sort of right is closing the barn door after the horse leaves.
But securing your personal data sounds a lot like a stone trying to gather up all the waves it makes when it drops in a pond.
Where do we draw the lines? Do we all end up walking around cloaks and masks in public and if you suss out who the faceless individual is next to you in the crowd it's your fault you figured it out?
This sort of right is closing the barn door after the horse leaves.
In fairness, so is the right to deletion.
Once your data is in some of these systems, it's sold on to other systems immediately. (Most of the "sell side" market is set up on the basis of subscriptions). So, for instance, your data gets written to some merchant system or whatever, and it's slurped out in the pull that happens 15 minutes later by data subscriber 531962. Unless you get your request to delete your data to the merchant customer support within that 15 minute time period, your data has already been pumped out into the ether.
Make it so you have to give affirmative consent to opt out of right to deletion? Great idea!
Of course, most of these companies slip the opt out language into the Terms of Service and Privacy Statement.
You, uh, you did read them before you clicked 'OK', right?
(BTW, you likely suspect that it doesn't take 15 minutes for these automated processes to slurp up new data. And, yeah, your suspicion is correct, on most of these systems, it takes far less than 15 minutes before one of their subscribers pulls new data. So. Yeah. Fun Times!)