For much of 2011, it looked like Android was crushing it. Google had brilliantly pushed its free mobile OS to every corner of the earth—you could pick up an Android phone from every manufacturer on every carrier at every price point, most often just as a consolation prize for signing a contract. Looking back, I’d peg Android’s high-water mark at around April Fool’s Day, when Fred Wilson declared Google’s OS to be the preeminent marketplace for mobile developers. Not only was Android nearing a majority share of the smartphone market, its rate of growth eclipsed that of every other platform. Meanwhile Apple’s growth appeared to have stalled; February 2011’s comScore data showed that even despite launching on Verizon, the iPhone was just barely holding on to its 25 percent market share.

The picture was clear: Android was running away with the mobile market. Google was unstoppable.

It’s funny to think about those days now, given everything that’s happened since. We had a summer of patent brawls that climaxed in Google scrambling to buy IP to shield its OS, including its enormous $12.5 billion purchase of Motorola Mobility. And then the fall and winter were dominated by a resurgent iPhone. comScore’s latest numbers show that while Android is still growing faster than its competitors, its rate of growth slowed markedly from February, while Apple’s has picked up. Nielsen’s new survey shows that the iPhone has nearly reached parity with Android. Among people who purchased a smartphone in the last three months, 44.5 percent chose Apple and 46.3 percent chose Google.

But the most obvious problem for Android appeared in just the last few days, when we saw stark, back-to-back earnings releases first from Google and then Apple. It’s not just that Apple’s profits—$13.06 billion for the quarter—now surpass Google’s revenues ($10.58 for the quarter). The bigger story is that Apple’s profits on the iPhone alone were probably around $9 billion last quarter, if you believe Sanford Bernstein analyst Toni Sacconaghi’s estimate that the phone makes up 67 percent of Apple’s profits. By comparison Google saw $3.51 billion in profits on all its operations. On just this single product line, then, Apple is making more money than Google makes on everything.

The numbers ought to ring alarm bells in Mountain View. They prove the folly of Google’s Android business model: Free and “open” (or clopen) may make money someday, but it’s hard to see how it’s ever going to make Apple-like profits.

It’s time for Google to try something radically different: Close Android. License it—you know, sell it in exchange for money!—to phone makers. Then, when the Motorola deal closes, instead of letting that money-losing firm operate independently (which Google has vowed to do in order to protect the tender sensibilities of its Android partners), the search company should send in its own hand-picked execs to transform the phone maker completely. I hear Jon Rubinstein is out of a job. Maybe he could be lured into coming on board to streamline Motorola’s chaotic product line-up—it now makes more than a dozen different Android phones—and to gin up the main thing Android needs, which is exciting and profitable devices.

You’ll think this idea is crazy. Android’s whole thing is being free; its no-cost appeal is one of the primary reasons that so many manufacturers chose it, and why they can sell their phones so cheaply.

But what has a free Android done for Google? Not much, really. According to Piper Jaffray’s Gene Munster, Google makes between $6 and $10 in ad revenue per Android user per year. That’s not nothing; going by the latest reported rate of 255 million new Android phones a year, that’s about $2.5 billion in revenue on Android. But that pales in comparison to Apple’s iPhone revenues ($20 billion in the last quarter alone).

What’s more, mobile ads aren’t proving to be the bonanza Google suspected they would be. As Henry Blodget notes, Google’s latest earnings proved that mobile ads are less profitable than desktop ads for the search company; as more people shift to mobile devices from desktops, Google could see its ad business decline. By licensing Android, Google could begin to extract even more money from smartphones—which, I thought, was the whole point of being in business.

Won’t licensing Android turn phone makers away from Google’s OS? That may have been a worry a few years ago, before manufacturers had committed to the OS. But now Google and major handset makers are stuck on the Android train. They’ve built their entire businesses around the OS, and many of their customers love it. And, anyway, phone makers know that Android isn’t really free in the first place—not to Google and not to handset makers. In addition to the cost of developing the OS, Google has lately been spending billions on patents to protect it. Nearly every handset maker, meanwhile, has signed licensing agreements with Microsoft to settle patent suits. Estimates suggest that each copy of Android costs phone makers $10 to $15 in licensing fees to Microsoft. That’s still a bargain—Windows Phone 7 costs $20 to $30 per copy.

So here’s Google’s opportunity: It could charge phone makers $10 per Android license, raising the total per-copy cost of Android to between $20 and $25. Sure, Samsung, HTC and others may balk, but what are they going to do about the added cost? Going to Windows would be more expensive and confusing to their businesses. As an inducement, Google could also begin settlement negotiations with Microsoft and other patent litigants to reduce Android’s licensing costs. Given all this, phone manufacturers would stick with Android—and Google would make a killing.

The bigger opportunity is for Google to use Motorola to create an iPhone of its own—a phone that everyone wants, that offers premium features at a reasonable price, and that can be sold at a steep profit. This is, of course, a very tall order. But it’s not impossible. Google has shown, with its Nexus line, that it knows how to create amazing gadgets. It also has enough resources to build an Apple-like manufacturing behemoth, and it can certainly afford to mount a marketing blitz.

Recently Larry Page has been doing his best impression of Steve Jobs. He loves gadgets that are “beautiful.” He remains silent in the face of criticism. He bluntly tells employees who don’t like his new strategy to go somewhere else. He’s not above playing hardball with his rivals—including by arbitrarily, capriciously keeping them out of his favored products.

So why not go all the way? In the phone business, the real money is in Apple’s model, in building and selling your own phones. Copy it.