Actually, I'd be happier if I knew of prognosticators who did put their money where their mouth is. Predictions accompanied by bid/ask spreads would be vastly more useful than predictions intended for immediate entertainment (ie, all the ones the pundit is unwilling to bet on).
As it is, though, there are just a few mildly popular websites that enable that.
Well, the counterargument to that is conflict of interest. Do I really trust the predictions of someone with financial interests in the outcome he's predicting?
I think there's a place for both types of reporting in our media. You've got Seeking Alpha for financial predictions by interested parties (who will at least disclose their interests, which is nice). Then you've got the mainstream media for general, ostensibly unbiased reporting and predictions.
(Experience has taught me that getting into a debate about the presence or absence of bias in the mainstream media is a classic blunder akin to starting a land war in Asia, or going in against a Sicilian when death is on the line. So I'll refrain from getting that started.)
The thing about trying to move the market by betting is that if someone calls your bs, you're ruined; and all it takes is one knowledgeable person with moderate resources (since you're putting out big odds and lots of money if you really want to influence things). Prediction markets have historically been extremely resilient against manipulation attempts.
As it is, though, there are just a few mildly popular websites that enable that.