I don't think this is practical. Say you need to get home at night. Without a phone, you can't call an Uber, you can't see if there's public transit still running (schedules have changed a lot over the past 1-2 years), you can't take pictures or videos of anything you witness, etc.
In theory with a basic phone you have some inferior options (like calling a cab company and praying until the cab arrives), but in practice the world has moved on.