You can stream if you want, but downloading is one of the highlights of it. I can download it at home and listen for hours at work or on a trip without dealing with poor or capped cell signal (or, like the majority of people in the US/world, without any data plan at all).
Perhaps because people often listen to podcasts in places where cellular may not be available? (planes, often subways, general dead spots) That said, I wouldn't object to a podcast app that updated the index but didn't actually download any titles; perhaps some can already do that. But the actual space taken up by the downloaded podcasts isn't usually a big deal.
I've been using git-annex as a podcatcher (http://joeyh.name/blog/entry/git-annex_as_a_podcatcher/) which is pretty nice and lets you update the index without actually downloading anything (using the --relaxed flag). It's set up to run periodically with launchd.
