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NEW YORK (Fortune) -- While the jury's out on President Obama's decision to sub Fritz Henderson for Rick Wagoner as CEO of GM, the shift doesn't matter because the bailout is suspect. The reason? Of all the models the federal government could have picked for restructuring the automaker, it picked Fannie Mae and Freddie Mac.

Usually when the government takes over a troubled business, it does so to manage an orderly liquidation of its assets. The feds routinely seize failed banks for this purpose, but Fannie and Freddie are different. They are publicly traded corporations in which the President appoints the CEO and several directors. The problems with that arrangement have been apparent for years, as Presidents of both parties have named to those boards politicos with no discernible expertise in mortgage finance. (For example, Rahm Emanuel, Obama's chief of staff, was a Clinton appointee to Fannie's board in 2000.)

After the 2004 scandal in which Fannie CEO Franklin Raines was accused of book cooking (he settled without admitting wrongdoing), people asked corporate governance authority Charles Elson for advice on how to fix those enterprises. "The first thing I told them was, 'You've got to get rid of the presidential appointment of directors,'" says Elson, who runs the University of Delaware's corporate governance center. But Fannie (FNM, Fortune 500) and Freddie (FRE, Fortune 500) didn't, and both companies failed.

Another problem with the Fannie and Freddie model is that the federal government gets to bypass the board, which would have to consider shareholders' interests in deciding what to do. That the GM (GM, Fortune 500) board screwed up in the past - as the boards did at all the companies in crisis - is beside the point. The legal representatives of GM's shareholders didn't have a say in the momentous changes at the top of their company. So bypassing GM's board sends an ominous message to anyone who owns - or might think of buying - the stock of any company that has received - or might need - government help.

That's a dangerous precedent. Because the government plays such a major role in Chrysler, AIG (AIG, Fortune 500), and Citigroup (C, Fortune 500), the CEOs and directors of those companies are effectively serving at the pleasure of the President. He didn't appoint them, but he could dispatch them just as swiftly as he did Wagoner. Instead of using the Fannie and Freddie model for GM, the administration should have operated through the board, sending the critically important message that shareholders and governance matter. And then - the hard part - the government should let the bankruptcy process, in which all players get a hearing, operate if necessary.

I asked Ira Millstein, the attorney for whom Yale's corporate governance center is named, what GM's directors are supposed to do at their board meetings - just call the Treasury Department for instructions? "That's what they do in China" was his response. "They make no bones about the fact that the commissars on the boards of these putatively private businesses really call the shots." This didn't seem like the most encouraging example. Do the directors have any role at all? "They're not completely useless," Millstein said. "They keep an eye on the business."

The fundamental conflict here is between what governance experts call insider and outsider systems. In the U.S. and Britain we have an outsider system: Ownership of our big companies is widely dispersed and separated from management.

What's happening at GM and potentially at other companies is a clumsy, conflicted attempt to impose an insider system, in which ownership is concentrated and controls management directly. That structure can work when the majority owner is an investor with a simple profit motive. But when government acts like the owner, it faces irresolvable conflicts between its roles as business owner and as business regulator and tax collector, or between its roles as profit maximizer and as representative of all the citizens - particularly those union members who live in Michigan and vote Democratic. It's a structure for which our economic, cultural, political, and legal systems weren't built. It won't work. Meaning we had better brace for more Fannies and Freddies.

--An earlier version of this story incorrectly stated that Rahm Emanuel was on the board of Freddie Mac. He was on the board of Fannie Mae. A corrected version is above.