I have used iTunes to create various Smart Playlists that contain podcasts using intelligent criteria (unplayed and most recently added podcasts; least recently played music + 3 hours of unplayed podcasts, etc.)
I am able to transfer these playlists to a 3rd generation iPod Touch running iOS 6.1, or a brand new Nano, and get the listening experience I expect.
When I sync the playlist to an iPhone 6, it creates an empty playlist on the device (if it were only podcasts), but the requisite podcasts show up in the Podcasts app. I had a similar problem with the iPod Touch years ago, but I was able to delete the Podcasts app. It looks as though this deletion is not possible on the iPhone.
Q: Can someone show me how to get a playlist containing podcasts to show up on a phone? TIA