Randy listens to TWiT podcasts with his Droid connected to his car dock, but his Samsung Galaxy S4 will not pass audio from the phone to the computer without bluetooth. Leo says that's odd that they've taken those features out. He suspects it's because of Bluetooth that they've taken it out via the USB port. An audio jack plugged into the dock could work, but he'll have an extra wire running.
It sounds like it's just a choice that Samsung and Google made. Randy went back to the Samsung Galaxy S3 to make it work and Leo says that's probably the best option if he wants to keep the phone hard wired. Stick with what works until he finds a modern phone that will do this.
The chatroom points to this article on how to enable USB audio on any Android 4 smartphone or tablet. Doctor Mom uses the same setup and says it's a device driver issue.