In reply to Jeremy Cherfas.

@eatpodcast @jimpick @realkimhansen @abrams @Feedly Jeremy, I agree with you wholeheartedly that SoundCloud is a dreadful option overall--apologies if I gave the impression otherwise. Given it's cost and the fact that it's what I would call a super-silo make it a non-starter unless you're looking for a very sort term solution or if you're a mega-media company and have the money to burn to try to reach another tiny sliver of audience you didn't have before.
Sadly, given their position in the space, companies like Apple, SoundCloud, and perhaps a few others haven't continued building out and innovating. (Marco Arment, who you mentioned in this particular podcast, recently had an episode on being "Sherlocked" that touches on the economics of perhaps why they haven't gone the extra mile http://boffosocko.com/2017/02/02/%F0%9F%8E%A7-under-the-radar-65-getting-sherlocked-under-the-radar/ ) Given the technology they've already got, they could/should go the next several steps to leverage their position to make things easier for everyone. The search and AI portions could also be done by Google, but presumably they'd need some additional motivation to do this as it's the type of niche area they've been getting out of lately. (And could we really take another GoogleReader-type shutdown?) Perhaps it might be a rich area for a feed reader company like Feedly to get into? Or maybe Jonathan Abrams with Nuzzel has some of the search/algorithm technology to be able to extend into this area, particularly for the discovery portion which Nuzzel is quite good at for articles.
We also need a better/easier solution for the average Jane who wants to create a simple podcast without spending two weeks doing a mini-startup to set it all up and get it going with the widest distribution possible.
I'm honestly puzzled that YouTube doesn't get into the space as they've already got a huge piece of the puzzle built. Just provide the ability to strip out an .mp3 file from a video (there's a huffduffer bookmarklet that allows this: http://huffduff-video.snarfed.org/ ) and make that available for download/subscription within their ecosystem. I'd suspect that with a week of coding, they could completely corner the entire podcast market from soup to nuts. One of the toughest parts of web is audio/video, and it's one of the few places that indie developers don't/can't touch because of the high technical and even intellectual property hurdles.
I do appreciate larger companies like This American Life doing things like Shortcut [https://m.thisamericanlife.org/blog/2016/10/introducing-shortcut ] though it would be better if the technology was opensourced. (See also thread at: https://twitter.com/rdhyee/status/809556321871622144 )
As an aside, I've just noticed at http://indieweb.org/podcast that Kevin Marks' ever useful unmung.com will apparently "turn podcast feeds into playable HTML5 audio with microformats markup".