I'm answering as a non-physician (business / CEO of our practice), so take this with a grain of salt...
I think there could be a market for you, depending on our location. However, where the real money is saved in the healthcare system is on same-day and acute care visits. That's at least where people end up realizing the value of membership - getting access to someone without extra charges (or much extra) compared to other places (urgent care centers, emergency room, etc.). Yes, you can argue that people should take care of themselves through preventive measures, but we can't always avoid injury or sickness.
The lifestyle medicine could come as a benefit and added value to what you're doing (and could even be the driving force of your practice), but rescuing someone from a $5,000 emergency room visit because you're available for stitching up their chin is pretty valuable.
If you're worried about being on call (which you shouldn't be, as the call schedules for DPC aren't bad at all), you could always make acute / urgent care medicine a different pricing tier.
I hope that helps! Best of luck to you!