Selecting a stream at a random time midprogram would work very well for content that has no past and no future and no logic or information, like a morning zoo show or a news show or sports coverage. I guess that stuff is called infotainment now.
That wouldn't work very well at all for maybe 90% of current podcast content. If the content were aggressively dumbed down, it might be possible to join in the middle, but then no one would listen to the dumbed down stream given an option of non-dumbed down podcasts.
Maybe another way of phrasing it is its like the difference between tuning into a random webcam at a random comedy sports, vs watching this weeks sitcom episode. The former is likely to be pretty funny but no idea what you'll get, and the latter has at least has an 18 minute long story, if not a longer series based story.
Personally, I do want to subscribe. I don't want Internet radio, I want podcasts.
That being said, autodownloading is still very useful and essential for me. Without podcasts, my subway commute would be infinitely more boring.