I was about to follow and delete the podcast app but noticed the following behaviours with the existing podcast app that should tide me through:
1) The podcasts do play one after the other. The default behaviour I had was "display newest to oldest" but "play oldest to newest". If I select a podcast from the bottom of the list it'll play through it, finish and then move onto the next one up the list. The order of podcasts is according to release date.
2) My playlist for audio podcasts was basically just to go through the list from oldest to newest and then get rid of any played podcasts. The "unplayed episodes" list was basically this, but in reverse order (newest to oldest). If I selected the one at the bottom (oldest) to play first, again it would work its way up the list as podcasts become played.
3) My main concern was being in the vehicle not being able to select podcasts without endangering myself. I loaded a 3rd party music player (Groove) and noticed that the playlists containing audio podcasts was still populated. It was just the music app that showed empty playlists. When I got to my car (Audi 2010 mmi) and plugged in my iphone, the behaviour was as before. The podcasts were still in the playlists, and I could specifically select podcasts from within the car's interface. It looks like they kept the API for external apps/devices to access podcasts intact.
I'm going to see if I can put up with it since I'm a sucker for punishment. It's great to know that the podcast app can be removed so I can revert everything to the way it was if it becomes too much for me.