Intelligence
An MTV article, of all things, supplies a possible answer to my question about why the US didn't knock out Iraqi broadcast capability:
Pentagon officials said they had intentionally waited to knock out the TV facility because its broadcasts were providing important intelligence about the state of the Iraqi regime.
Given that there's still widespread uncertainty over whether S.H.'s broadcasts were prerecorded or not, I'm not sure what intelligence it provided; but of course that doesn't mean it's not useful to people who know more about this stuff than I do. I'm just being an armchair pundit. If that's not too redundant.
Anyway, the other relevant item in that article, from the same paragraph, is this:
U.S. missiles or bombs pounded Iraq's television and telecommunications hub in Baghdad late Tuesday. The international satellite feed of the country's television network has since gone off the air. But within Iraq, national TV has broadcast intermittently since the strikes.
So the US has knocked out Iraq's ability to broadcast internationally, but not locally. Perhaps it's harder to destroy broadcast facilities than I thought; I suppose that's a kind of a comforting thought.