Instead, what they want is to selectively groom what the internet "remembers" about them. Remove the bad, keep the good.
Fortunately their newer reviews are so glowing that they still get over 4 stars average and their front window is covered in plaques of their awards and their most recent 5/5 health inspection (in the UK its quite common for restaurants to flaunt their 4/5 or 5/5 health report on their front door as advertising - there is no legal requirement to show it except in the city of Hull where now almost every restaurant now has at least 4/5 rating as a consequence given the death sentence that a something below 3/5 represents).
Couldn't identity fraud be better handled if we had a system in place for it though? "Oh, my identity was stolen. Time to get a new one!"
When a disgruntled ex publishes a page saying you have a bunch of STDs[1], or a company crawls your social media info and starts using it to market some product without your conscent, and these are the first things your cutomers (and/or friends) see when they google you... you're happy takedown requests are a thing and there are laws to protect you.
That's basically what all these European "privacy" laws are amounting to.