You can't engineer this sort of thing away. A business that gets 1000 of these letters will have to hire someone to handle it, regardless of how good a job they did designing things.
Wrong. Even if I didn’t store anything besides absolutely necessary (does your product involve usernames or emails - bam, personal information) and was absolutely above board, it would take me hours to respond to this.
You see: you should have read the law before assuming that requesting this information from the user is legal. It had to be stored in one, single place. Therefore answering this question shouldn't take more than 5 minutes, if you have anticipated GDPR.
What about their employees? Aren't employees, or ex-employees, also entitled under GDPR to be informed about what personal data the company stores or processes? Honest question!
I mean, if those records are being kept, it shouldn't be that hard to make them easily user-accessible, right? Support people that got the letters could just give users the link to the page with the data.
It seems to me that could easily create a privacy issue of its own. Certainly just a link would be terribly insecure, you'd need to authenticate the user. And whatever you do, you've now created a web-facing portal to the private data you're supposed to protect. Seems risky to me.
My company (Aptible) makes a product called Gridiron that does this. All of the data that a requester is entitled to can be pre-structured and organized in a source of truth. That's what Gridiron is.
The answer is going to be automation. You don't hire a person to physically handle each of those 1000 requests, just like you don't have someone typing in each employee's pay stub and calculating their tax withholdings.