Structure is an editing problem, but there are lots of people who listen to podcasts sped up, or with silences removed. Apps like Overcast will do this for you.
Some podcasts, like Hardcore History, are worth the 5 hour runtime and they're so rarely published it doesn't really matter.
Structure is an "editing problem" but once you go beyond a fairly straight interview or talk show format, the amount of post-production work increases dramatically. With the help of some automation, I can edit a 20 minute interview in an hour so so. Structuring a 1 hour show from different clips and inserting various breaks etc. would probably add a good day to the whole process.
When I say it's an editing problem, I mean it's not something you can easily change as a consumer. On the other hand cutting out silences and speeding up slow speakers is something you can fix 'in post' using a generic podcast app.
I'm carrying around my a junked iPhone 5C and using it just for Overcast. I haven't been able to find any podcast players on Android that work as well for me. If I could find one, I could stop carrying two phones.
I've been a fan of PocketCasts. Lots of people recommend podcastaddict because it's free and has a million knobs, but I enjoy the comparatively slick interface of PocketCasts.
I'm personally a fan of PocketCasts but with a small caveat: Syncing feeds goes through their servers, which means smaller feeds aren't updated instantly, even when manually syncing.
I'm going to give PocketCasts a try. Overcast was pretty much a perfect app for me. If I can't find something I like as much on Android, Overcast might be the killer app that makes my next phone an iPhone.
I find antennapod decent (and open source). To be honest, it might be wise with something in the cloud that can keep tabs on what episodes you have listened too. Most do it locally and it is easily forgotten when switching devices.
Some podcasts, like Hardcore History, are worth the 5 hour runtime and they're so rarely published it doesn't really matter.