Is it possible to conduct some kind of denial of service legal attack against an unprepared business through the use of GDPR letters?
And at the end of the day, you'll have to get sued for taking too long to respond, at which point a judge will investigate and can then tell that those requests were not legitimate.
Long answer: people actually tried to do it to Facebook, Google, etc. As a response, they each started offering self-service tools to download your data.