No, Eric Schmidt didn’t step down from being CEO of Google to take Steve Jobs’s position at Apple. I’m fairly certain Schmidt was demoted. Or if he wasn’t, then he should have been.

From a strict business perspective I suppose it’s ridiculous to criticize Schmidt’s performance at Google, but that won’t stop me. The guy has done a fabulous job of optimizing search and web advertising but nearly everything else he and Google have done has been a failure. What else does Google make money from other than search and ads?

Nothing.

Yeah, but YouTube is almost profitable, right?

Hardly. While YouTube may be operating at near break-even that completely ignores the minimum $5 billion sunk and lost in the video sharing venture over the last several years. YouTube is still years from breaking-even on a net-net basis.

But the real killer for Eric Schmidt — the bonehead move that would have gotten him fired had I been on the board — was that $6 billion offer for GroupOn.

Here’s what Google could have done — should have done. First, take four top engineers and set them up like a startup in a rented apartment, denying them any access to the Googleplex. No free massages and definitely no unlimited Froot Loops. Google has grown to the point where it is virtually impossible to get anything done. So just like IBM did with the PC, a GroupOn clone would have to be done as a completely separate renegade operation. Four engineers, two months, and GoogleOn would be ready to go.

Then simply pay every adult in America $10 to join.

That’s about 100 million members or $1 billion. See, I saved Google five billion dollars.

It’s actually even better than that since GroupOn has only 50 million members.

Buying companies yields far more instant advantage than building them, I know. In Groupon’s case Google would get effectively irrelevant, copyable technology along with their entire user base. But $6 billion? Really?

My plan is way better.

Trying stuff that “doesn’t work” until “something does” is awesome. But seriously, when will the “something does” part begin for Google? The company is so financially successful because of its one trick, but at some point even at Google there is ultimately someone to blame. In this case that’s Eric, not so much for offering GroupOn $6 billion, but for getting turned down. The offer stinks of desperation and impotence. And to be rejected makes it even worse.

We can definitely say Eric did not screw-up search, but can we say anything else? Remember when Microsoft “missed” the internet? Well Google “missed” the Facebook.

Now understand that for all my complaints Google is going nowhere but up, with the economy slowly recovering and with that Internet advertising. But I’d say Eric had his shot. Unfortunately Larry Page probably isn’t the hammer Google needs, either. Google has super people but a lot of them seem to be in a rut. If Larry could have changed that, wouldn’t he have already done so?

I don’t know who should be the next CEO of Google, but I know who I’d hire to be the next head of Google HR.

Yahoo’s Carol Bartz.