Outsourcing paid search to Google sounded like a panacea to some who have followed Yahoo’s travails, but antitrust concerns probably ended that discussion.

If you ever had what seemed like a terrific world-beating idea, something so cool that it had to work, and then woke up the next morning realizing the incredibly painful bad points to the idea, you understand the revelation that took place at Google. Feel free to think of it as a blast of cold water right in the face.

The sobering prospect of dealing with the Federal Trade Commission over antitrust issues again likely gave Google pause. Though CEO Eric Schmidt had offered whatever help he could to Yahoo as it fights Microsoft’s takeover bid, in reality they couldn’t help as much as Google would like.

Taking over Yahoo’s paid search business and adding it to Google’s already-dominant position could have profited Yahoo well. The Wall Street Journal said the early enthusiasm about those prospects faded this week.

One can imagine a dreamy-faced Schmidt pondering Yahoo’s paid search business at the Internet’s busiest web property. Picture top Google lawyer David Drummond entering the picture, whispering more and more urgently into Schmidt’s ear, until the dream ends and Schmidt’s expression changes into that of someone who has rapidly sobered up at the sight of flashing red police lights.

Google still hasn’t finished its DoubleClick acquisition, as European regulators proved less pliable than their FTC counterparts. Though current evidence suggests European approval should arrive on or before early April, Google doesn’t appear interested in what would be an even bigger battle for Yahoo’s business.