My understanding is that if someone is not a customer, and I hold no data on them, then I can safely ignore any requests. At worst I can automate a response saying "I hold no data on you".
For customers, how many requests would you expect? One in 100? One in 1000? If I store the data securely, and I only use it for the purpose it was intended, I can automate a response that (a) Sends them a copy of their data, (b) points them at the privacy policy saying I don't do anything unexpected with their data, and (c) offer a link to delete their data.
Once set up, these should not place a significant burden on the provider of a service.
I suspect we are arguing about how much work will be required. I'm saying that once set up, the administrative overhead is negligible, you are saying it isn't. Certainly the services I run have seen no increase in administrative load, I'd be interested to know who has seen a significant increase (once already set up) and why.