Here is my solution: I get paid by the minute by anyone who calls me, I get to set the rate. The phone company may have a cut of this as an incentive to make it work. Also, I may refund your money if I decide you didn't waste my time.
You want to try to sell me something? Great, at $10 / minute I'll listen to you.
OK, but I see a problem with your doctor calling you. If it's pay-to-call, I have a sneaky suspicion what the American medical system would do to turn that into a billable event. And unfortunately doctors offices do still call, they are one of the only sectors that still uses fax machines after all.
As long as there's a system to whitelist specified numbers of ahead of time to be free, I think it would work out. Companies would just tell customers ahead of time what number they'd be calling from
You want to try to sell me something? Great, at $10 / minute I'll listen to you.