Flexibility is cool. I have recently found some doctors willing to communicate with my by e-mail, which is asynchronous, but most still fear HIPAA to the point where they limit what they will say there.
So how can a clinic make change happen? As Ralston says, by putting themselves in their customer's shoes. But also, by first automating the specific services patients use most.
If your practice issues a lot of prescriptions, and patients have complained of mistakes or cost, maybe you want to push eprescribing, which replaces a prescription pad with a checked form and can have the order waiting at the pharmacy before the patient arrives there.
If you're doing a volume business, with a waiting room that looks like a cattle drive, maybe you had best first automate your appointment system. If you're specializing in referrals, that's where you look first.
In all these efforts, you need to play Undercover Boss and look at your operation from the patient's point of view. How are they doing these things now? How do they want to do them?
Instead of seeing what you do as a service, in other words, see what you do as a business. Instead of seeing IT as a cost, make it a benefit. Do those things that provide the most customer satisfaction first, and the rest should take care of itself.