I don't use a smartphone, and while I'm familiar with podcasting apps from my tablet and my wife's Android phone, what I would like is the functionality that used to be common in stand-alone media players such as the iPod and Sansa lines. Simply put, files that have a genre or location that gets read as "audiobook" or "podcast" would be treated a little differently. They would not show up in music shuffle, they would have the ability to speed them up or slow them down (without that being a system-wide switch), and they would automatically get a bookmark when you left any specific podcast file, so you could listen to music and then go back to the podcast (or audiobook) and resume exactly where you were without any special effort.
These functions do not require any sort of major heavy lifting, as one would find in a full-fledged podcasting app. There's no need to download or convert or parse an RSS feed. Just recognize that audio books and podcasts are not music, and give a few small features to reduce the effort of switching between music and spoken word. I'm actually astonished that DAPs seem to have lost these features that once were touted as being so awesome and amazing and useful.