I don't think you're really missing anything beyond the fact that podcasts have diversified to the point that you can find one in whatever niche you're curious about. There's also a huge array of artistic and fiction content, with a panoply of sound styles.

The problem, of course, is finding the niche that fits you. It's classic long-tail stuff. I'm sure there are lots of podcasts that sound like indie radio stations, though I have no idea how you'd go about finding them except by trial and error (and referral).

Once you find it, the medium is conveniently offline, requiring neither airwaves nor a live connection -- as well as the ability to speed it up or slow it down, skip, etc. If nothing else, I suspect a lot of those indie stations make their material available by podcast, which would give you access to similar content from all over the world.