You'd probably do better to target businesses than consumers. Sure, you don't want to call the pharmacy, but how much are you really willing to pay to save yourself one phone call once a month? (Beware, if you're a highly paid and highly antisocial HN user, your response to this is probably going to be "a lot more than the average customer".) Same problem for the restaurant call.
On the other hand, how much would your pharmacist be willing to pay to save his highly paid staff the four hours they spend on the phone every month reminding customers that the prescription they've ordered has been in for a week now? Find a way to solve problems for businesses, not consumers.
I suspect automated collection calls are illegal, or otherwise already exist, but if they're not and they don't, that sounds like a way to make absolute piles of cash from collection agencies (in a slightly ethically dodgy way).
Why not start with the customer first?
Ask them questions to uncover their workflow...then pose questions like "what really makes you want to pull your hair out when it comes to doing xyz"...
Also at the OP said, any thing that involves communicating with phone + manual work - things businesses are already doing - are opportunities (potentially)
A service to automatically call the pharmacy and request a refill. (I hate having to call every month)
A service to call a restaurant for you and find out how long the wait is.
A service to make automated collections calls for businesses.