Note that I don't understand how a podcast is different from a radio show that somebody recorded on a computer, so maybe I'm missing key functionality.
Which is why podcasters don't have any good statistics.
I recommend listening to the Startup podcast, they do a great job of explaining how the industry works :)
You can barely track how many people download, let alone listen, when they stop, etc. All the things advertisers want to know.
Well, F them.
Since the audio data is coming from servers that are under our control, we can get interesting data like the amount of bits that have been downloaded / streamed by a specific client. It's not perfectly accurate, but there is some tricks you can do just by matching the user agent + ip + the bits requested. You can for sure get a better picture than just knowing that someone has downloaded an episode.
And yes, advertisers want to know everything, but at the same time, are clicks on banners an accurate way of knowing if people are really interested in your ads? Can you say that people really watch all the TV ads and do not go to the toilet instead? These are tough problems to solve, yet there are some approximations that should be good enough.
There are lots of Podcasts on SoundCloud.
It's still a hard thing to integrate an RSS feed into a modern website...RSS is only really popular with podcasts and hasn't had much development in a while. Working with XML sucks.
Libsyn and Blubrry manage this part for you (having an RSS feed that is also a site's content and does tracking) but you're limited to hosting on their sites, wordpress or needing a developer.
There's a lot of room for improvement here.