Podcats (I use Overcast) are pretty different from music and I wouldn't generally intermix them. And you already have Library and Streaming modes of Apple Music so podcasts would be yet another mode.
The things is that iTunes also allows you to manually reclassify you media files as a podcast, and I found (still do, actually) that very useful for managing my collection of radio comedy scrounged together from all sorts of places (downloads from BBC iPlayer, downloads from various places collecting that kinds of shows, a very few genuine podcasts). That way I could keep them out of the main music library, gain the listened/unlistened episode display and playback position tracking, and still easily sync them over to my phone [1].
Without iTunes, I would have to set up some fake local podcast feed on my computer to get those episodes into the podcast app of my choice instead.
[1] Using iSyncr + Rocket Player after switching from an iPod to an Android phone – sadly those apps were sold by the original developer two years ago, though, and the new owners are seemingly just trying to turn them into a cash grab, so I cannot recommend them any more, though for now the old versions sort of keep working, albeit you need a rooted phone to work around some issues.
On the other hand Apple Music already has audio streaming and playback and a Library mode so should Podcasts write their own?
While yeah debundled separate apps will make probably the main use case of what was the bundled app better it also likely leads to stagnation and buggier experiences over time in the apps where the less popular features were debundled into.
Like all knowledge and talent required to code the Audiobooks app is the same as whats required to code the Music app so which team would you rather be on given the choice.
Without iTunes, I would have to set up some fake local podcast feed on my computer to get those episodes into the podcast app of my choice instead.
[1] Using iSyncr + Rocket Player after switching from an iPod to an Android phone – sadly those apps were sold by the original developer two years ago, though, and the new owners are seemingly just trying to turn them into a cash grab, so I cannot recommend them any more, though for now the old versions sort of keep working, albeit you need a rooted phone to work around some issues.