He’s barely dipped his toes in the TV waters. But already, outgoing Google CEO Eric Schmidt is getting laughed off the airwaves.

The rumor, courtesy of the New York Post, is that Schmidt is pursuing a post-Google career as a TV talk-show host. (He announced last week that he was stepping down as CEO effective April 4.) Google and Schmidt wouldn’t comment for the story, but the Post has collected convincing details — namely, that CNN producer Liza McGuirk helped Schmidt film a pilot.

Is no one picking up the irony here? At Google, Schmidt has made a career of overturning old media models. Why isn’t he aiming to follow in Lonelygirl15’s footsteps and become a star on YouTube? After all, he spent $1.65 billion of his shareholders’ money on it. He might as well give it a whirl. Literally, nothing’s stopping him. Isn’t that the point of broadcasting yourself — that you don’t need a CNN producer’s help to reach millions? And isn’t that why Google — from Schmidt on down — has been pushing Google TV so hard?

But one could make the same argument for Blogger, the blog-publishing tool Google acquired much earlier in Schmidt’s tenure as CEO. Schmidt, with the prestige of Google behind him, could have ruled the blogosphere by now.

The truth is Schmidt is enamored of conventional media. He’s long railed against blogs and other online publishers, dismissing their output as a “sewer.” And in his new role as executive chairman, he’s going to continue his media-schmoozing role, as Google’s ambassador to the olds.

No wonder Google is flailing to find a social strategy: Its CEO of the past decade has notably abstained from using all the new publishing tools his company has enabled. (His feeble Twitter output barely deserves notice.)

Schmidt’s media obsession is a bit of a shame. He may not be TV-host material, but he’s clearly a brilliant thinker on green issues and a backer of clever startups. Those are both more promising post-Google career venues for him.

If he soldiers on with this TV attempt, he may soon be facing a harsh reality: Absent his title of CEO, no one may want to pay attention to what he has to say. And given his track record of putting his foot in his mouth, perhaps that’s a good thing.