Yahoo are giving away money? No, of course not. So how does your logic apply. People are visiting Yahoo because they want to use Yahoo services ... even if they're not then they're still visiting, that is valuable to online businesses where a lot of marketing goes in to just getting visitors.
> it would amass an amazing number of visitors, but would be a worthless business. //
You'd get in serious debt. But the website would still be worth something afterwards, not what you paid, but it would have a significant value. Good marketing could convert some of those repeat visitors looking for free money. Indeed, it actually sounds like not a half bad idea! Give away money via paypal/bitcoin or some such up to a limit for a few days, network effect is going to amplify that, then stop and lay out your stall .. if your stall was using bitcoin/paypal for micro payments then double+plus+good! You'd have stories in press around the world, everyone would be sharing your site ("Hey I got free money 2 days in a row at example.com").
Want to cause a riot? Release $100k in $1 notes in public in a busy, large, public space (Central Park?). Say you'll be back next week ... how many millions of people do you think you could attract, how many the 3rd week!!? How much would the press coverage and whatever brand association you could muster be worth?
Anyway, I digress.