What provisions are there in place for a company receiving this type of request to confirm the identity of the requesting party? Are companies expected to be able to properly identify a citizen, in order to not disclose possibly very sensitive information to someone else impersonating them? In a lot of cases the company might not even have enough information stored in order to know who the owner of a given account is. How do you prove "abc123@example.com" is Mr. Smith, if your service doesn't ask them for names? Or if it does, which Mr. Smith do you have on record? Email original senders can be spoofed.
The first thing I'd do if I was a black hat type attacker would be to submit GDPR information requests to all internet companies I could think of in behalf of all my targets.