Vlad A service like that would be helpful for removing it from the origin, and keep it off on an ongoing basis.
However it seems to be that even after completely removing the data from these websites, it is still showing the personal contact info directly on Kagi's website because it is in the link title and description.
The contact information is either stored directly on Kagi's server, or there is a cache it is picking up from a partner index that is unrelated to the original website.
Google has the ability to request personal information like this to be removed:
https://support.google.com/websearch/troubleshooter/3111061?hl=en&ref_topic=3285072&sjid=10603885210559377011-NA
It may be that eventually the web crawler would update it, but that could take awhile. Another problem is that some of the most malicious sites do not care about privacy laws and will not remove the info ever, or want thousands of dollars in blackmail.
I do not know if legally a John Smith could request to remove everything with his name in the EU. The problem is mostly when it includes a name plus phone number, email, and/or home address displayed directly in search results. This would rule out the other John Smith's who would not share that info.